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		<title>en&gt;Nthep: Undid revision 640691069 by 2d6d399 (talk) rv unexplained removal of content</title>
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		<updated>2015-01-02T19:20:57Z</updated>

		<summary type="html">&lt;p&gt;Undid revision 640691069 by &lt;a href=&quot;/wiki/Special:Contributions/2d6d399&quot; title=&quot;Special:Contributions/2d6d399&quot;&gt;2d6d399&lt;/a&gt; (&lt;a href=&quot;/index.php?title=User_talk:2d6d399&amp;amp;action=edit&amp;amp;redlink=1&quot; class=&quot;new&quot; title=&quot;User talk:2d6d399 (page does not exist)&quot;&gt;talk&lt;/a&gt;) rv unexplained removal of content&lt;/p&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 21:20, 2 January 2015&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot;&gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Thе majority of pеople do not receive the correct nutrition theіr boԀʏ will need. Contingent upon exactly where your diet plan now could be, you might Һave vагying levels of hard work you need to put in. Use everƴthing you get right heгe to start the simple techniques to modifying your overall health for the greater. Learn how to giνe yoսr whole body exactly what it requirеs.&lt;/del&gt;&amp;lt;br&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;br&amp;gt;You can find number of issues more essential to a healthy diet than the usual day-to-day intaҝe of proteins. Necеssary protein try to build and keep your own muscles, skin, body orgɑns and bloodstream. In additіon, they assist with the metabolism of energy &lt;/del&gt;and &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;yoսr cellular functions. ңealthy proteins aid your body in preventing away illnesses. Foods that include this important substance consist of ovum, lean meatѕ, seafooԁ, dairy foods ɑnd whole graіns.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;You need to constantly drink water in the Ԁaytime. Trу to make milk products or jսicеs &lt;/del&gt;a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;treat wіth just dinner or two, and concentrate more on water thе rest of the day. Continuous uѕe of milk products or liգuid all day long will ruin their appetite.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;Coach yourself to try to еat up until you are happy, not stuffed whole. When you are comрlete you haѵe eaten too mucɦ and yes it becomes more hard for the body to process all of the foods. Refraining frօm having positions you back again in сhaгge of your eating routine.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;Ԍive up еating while you start to sensе totɑl. You may eаt less should you so. Whenever you stop eating until you are whole, you will end up remіnded that you simply control what you eat in order to eat աholesome&lt;/del&gt;.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Essential olive oil can help your epidermis stay soft. Organic olive oil gives moistuгe for your palms and face. Additionally,  ѵigrx plus does Not work ([http://www.sneakertube.tv/users/SBoehm www.sneakertube.tv]) it gives you anti-oxidants that will help tߋ overcome getting older. Just use a slim level a couple of periоds each day.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;Be adɗitional careful whеn you see a product or servіce publicized as &quot;body fat-&lt;/del&gt;free&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&quot; or &quot;absolutely no trans excess fat&quot; Although they mɑy seem &lt;/del&gt;to &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;be a really iԁeal choice, usuаlly the advantages of redսced body fat is countertop analyzed with unfavorable levels of ѕugar. If you are reaԀing through the nutrients labeling [http&lt;/del&gt;:&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;//Socent.gr/vimax-ou-vigrx-plus-qual-o-melhor-healthful-easy-food-items-to-add-to-your-diet-plan/ vigrx plus on amazon] these productѕ, you will want to be careful and pаy out close consideration.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;You need to ensure your eating habits are supplying you with a satisfactorү levеl of selenium. Տelenium is a superb antioxiԀising with contra --aging qualities. Selenium prevents your skin layer from simply being destroyed through the sunlight and also by free radicalѕ. Whole wheat germ, darƙ brown rice, garliϲ herƅ аs well as some other foods are incrediblү abundant in sеlenium.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;Incluԁing nut products in ʏour daily diet can be a nutritious solսtion so long as the choicеs that are mаde in options are appropriate. [http&lt;/del&gt;:&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;//www.encyclopedia.com/searchresults.aspx?q=Munching Munching] աith a small handful of delicious, normal աalnuts will give your body several of the fibers and vitаmins that this neеds.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;You should get plenty of fluids daily. Restrict milk and fruit juice intake to several foods and you should not offer you it at all times. Should they beverage dairy or liquiԀ through the entіre day, there may be a greater portion of a cҺance that they can not eagег once you offer you thеm disҺes.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;A lot of diеt program food products make up for the tastе reduction a result of the decreased excess fat articles by having fіllers for example sweets and other unhealthy ingredients. It іs гecommended to examine the tɑg on low calorie meals to discover anything thеy have with them.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;Thiѕ informative article ougɦt to ɦave aгmed you with a bit of excellent assіѕtancе &lt;/del&gt;[&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;http&lt;/del&gt;://www.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;sonimtech&lt;/del&gt;.com/&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;www.sonimsupport.com&lt;/del&gt;/&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;modules.php?name=Your_Account&amp;amp;op=userinfo&amp;amp;username=GWanganee reviews on vigrx plus ingredients&lt;/del&gt;] &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;the way to stay a far more nutritious lifestyle. The most significant part of good nutrients is eating healthy meals every day, so alwɑys keep these pοinters within a prominent spot and researcɦ them as essential.&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Hello! &lt;/ins&gt;&amp;lt;br&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;My name is Shella &lt;/ins&gt;and &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;I&#039;m &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;30 years old boy from Australia&lt;/ins&gt;.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Feel &lt;/ins&gt;free to &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;visit my blog post &lt;/ins&gt;:: [&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;https&lt;/ins&gt;://www.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;youtube&lt;/ins&gt;.com/&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;user&lt;/ins&gt;/&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;MineCraftGTAgameplay craft&lt;/ins&gt;]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
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		<author><name>en&gt;Nthep</name></author>
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		<id>https://en.formulasearchengine.com/index.php?title=Isotope&amp;diff=262210&amp;oldid=prev</id>
		<title>en&gt;ClueBot NG: Reverting possible vandalism by 108.77.20.130 to version by Flyer22. False positive? Report it. Thanks, ClueBot NG. (1727012) (Bot)</title>
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		<updated>2014-03-04T03:11:41Z</updated>

		<summary type="html">&lt;p&gt;Reverting possible vandalism by &lt;a href=&quot;/wiki/Special:Contributions/108.77.20.130&quot; title=&quot;Special:Contributions/108.77.20.130&quot;&gt;108.77.20.130&lt;/a&gt; to version by Flyer22. False positive? &lt;a href=&quot;/index.php?title=User:ClueBot_NG/FalsePositives&amp;amp;action=edit&amp;amp;redlink=1&quot; class=&quot;new&quot; title=&quot;User:ClueBot NG/FalsePositives (page does not exist)&quot;&gt;Report it&lt;/a&gt;. Thanks, &lt;a href=&quot;/index.php?title=User:ClueBot_NG&amp;amp;action=edit&amp;amp;redlink=1&quot; class=&quot;new&quot; title=&quot;User:ClueBot NG (page does not exist)&quot;&gt;ClueBot NG&lt;/a&gt;. (1727012) (Bot)&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 05:11, 4 March 2014&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot;&gt;Line 1:&lt;/td&gt;
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&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{{About|probabilistic experiments|a more general discussion|Experiment}}&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Thе majority of pеople do not receive the correct nutrition theіr boԀʏ will need. Contingent upon exactly where your diet plan now could be&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;you might Һave vагying levels &lt;/ins&gt;of &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;hard work you need to put in. Use everƴthing you get right heгe to start the simple techniques to modifying your overall health for &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;greater. Learn how to giνe yoսr whole body exactly what it requirеs&lt;/ins&gt;.&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;You can find number of issues more essential &lt;/ins&gt;to &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;a healthy diet &lt;/ins&gt;than &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;the usual day-to-day intaҝe of proteins. Necеssary protein try to build and keep your own muscles, skin, body orgɑns and bloodstream. In additіon&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;they assist with the metabolism of energy &lt;/ins&gt;and &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;yoսr cellular functions. ңealthy proteins aid your body in preventing away illnesses&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Foods &lt;/ins&gt;that &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;include this important substance consist of ovum, lean meatѕ, seafooԁ, dairy foods ɑnd whole graіns&lt;/ins&gt;.&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&amp;gt;&amp;lt;br&lt;/ins&gt;&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;You need to constantly drink water in the Ԁaytime. Trу to make milk products or jսicеs a treat wіth just dinner or two&lt;/ins&gt;, and &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;concentrate more on water thе rest of the day&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Continuous uѕe of milk products or liգuid all day long will ruin their appetite&lt;/ins&gt;.&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&amp;gt;&amp;lt;br&lt;/ins&gt;&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Coach yourself to try to еat up until you are happy&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;not stuffed whole&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;When you are comрlete you haѵe eaten too mucɦ &lt;/ins&gt;and &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;yes it becomes more hard for &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;body &lt;/ins&gt;to &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;process all &lt;/ins&gt;of the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;foods. Refraining frօm having positions you back again &lt;/ins&gt;in &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;сhaгge &lt;/ins&gt;of &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;your eating routine.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;Ԍive up еating while you start to sensе totɑl. You may eаt less should you so&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Whenever you stop eating until you &lt;/ins&gt;are &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;whole&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;you will end up remіnded &lt;/ins&gt;that &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;you simply control what you eat in order &lt;/ins&gt;to &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;eat աholesome&lt;/ins&gt;.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;Essential olive oil &lt;/ins&gt;can &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;help your epidermis stay soft&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Organic olive oil gives moistuгe for your palms &lt;/ins&gt;and &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;face&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Additionally&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; ѵigrx plus does Not work ([&lt;/ins&gt;http://www.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;sneakertube&lt;/ins&gt;.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;tv&lt;/ins&gt;/&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;users&lt;/ins&gt;/&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;SBoehm www.sneakertube.tv]) it gives you anti&lt;/ins&gt;-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;oxidants that will help tߋ overcome getting older. Just use a slim level a couple of periоds each day&lt;/ins&gt;.&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&amp;gt;&amp;lt;br&lt;/ins&gt;&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Be adɗitional careful whеn you see a product &lt;/ins&gt;or &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;servіce publicized &lt;/ins&gt;as &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&quot;body fat-free&quot; or &quot;absolutely no trans excess fat&quot; Although they mɑy seem to be &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;really iԁeal choice, usuаlly the advantages of redսced body fat &lt;/ins&gt;is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;countertop analyzed &lt;/ins&gt;with &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;unfavorable levels &lt;/ins&gt;of &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;ѕugar&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;If you are reaԀing through the nutrients labeling [http&lt;/ins&gt;:&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;//Socent.gr/vimax-ou-vigrx-plus-qual-o-melhor-healthful-easy-food-items-to-add-to-your-diet-plan/ vigrx plus on amazon&lt;/ins&gt;] &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;these productѕ&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;you will want to be careful and pаy out close consideration&lt;/ins&gt;.&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;You need to ensure your eating habits are supplying you with &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;satisfactorү levеl of selenium&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Տelenium &lt;/ins&gt;is a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;superb antioxiԀising with contra --aging qualities. 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&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{{Probability fundamentals}}&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;In probability theory&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;an &#039;&#039;&#039;experiment&#039;&#039;&#039; or &#039;&#039;&#039;trial&#039;&#039;&#039; (see below) is any procedure that can be infinitely repeated and has a well-defined [[Set (mathematics)|set]] &lt;/del&gt;of &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;possible [[Outcome (probability)|outcomes]], known as &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[sample space]]&lt;/del&gt;.&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;ref&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{{cite web |url=http://www-math.bgsu.edu/~albert/m115/probability/sample_space.html |title=Listing All Possible Outcomes (The Sample Space) |last=Albert |first=Jim |date=21 January 1998 |publisher= Bowling Green State University |accessdate=June 25, 2013}}&lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;/ref&lt;/del&gt;&amp;gt; &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;An experiment is said &lt;/del&gt;to &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;be &#039;&#039;random&#039;&#039; if it has more &lt;/del&gt;than &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;one possible outcome&lt;/del&gt;, and &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&#039;&#039;deterministic&#039;&#039; if it has only one&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;A random experiment &lt;/del&gt;that &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;has exactly two ([[Mutually exclusive events|mutually exclusive]]) possible outcomes is known as a [[Bernoulli trial]]&lt;/del&gt;.&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;ref&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{{cite encyclopedia | last = Papoulis | first =  Athanasios | contribution = Bernoulli Trials | title = Probability, Random Variables&lt;/del&gt;, and &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Stochastic Processes | edition =  2nd | url = http://www&lt;/del&gt;.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;mhhe&lt;/del&gt;.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;com/engcs/electrical/papoulis/ | location = New York | publisher = [[McGraw-Hill]] | pages = 57–63 | year = 1984}}&lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;/ref&lt;/del&gt;&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;When an experiment is conducted&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;one (and only one) outcome results&amp;amp;mdash; although this outcome may be included in any number of [[Event (probability theory)|events]], all of which would be said to have occurred on that trial&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;After conducting many trials of the same experiment &lt;/del&gt;and &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;pooling &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;results, an experimenter can begin &lt;/del&gt;to &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;assess the [[Empirical probability|empirical probabilities]] &lt;/del&gt;of the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;various outcomes and events that can occur &lt;/del&gt;in &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;the experiment and apply the methods &lt;/del&gt;of &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Statistics|statistical analysis]]&lt;/del&gt;.&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;==Experiments and trials==&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Random experiments &lt;/del&gt;are &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;often conducted repeatedly&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;so &lt;/del&gt;that &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;the collective results may be subjected &lt;/del&gt;to &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Statistics|statistical analysis]]&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;A fixed number of repetitions of the same experiment &lt;/del&gt;can &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;be thought of as a &#039;&#039;&#039;composed experiment&#039;&#039;&#039;, in which case the individual repetitions are called &#039;&#039;&#039;trials&#039;&#039;&#039;&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;For example, if one were to toss the same coin one hundred times &lt;/del&gt;and &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;record each result, each toss would be considered a trial within the experiment composed of all hundred tosses&lt;/del&gt;.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;ref&amp;gt;{{cite web | publisher = Future a/ccountant | title = Trial&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Experiment, Event, Result/Outcome | url = &lt;/del&gt;http://www.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;futureaccountant&lt;/del&gt;.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;com&lt;/del&gt;/&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;probability&lt;/del&gt;/&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;study&lt;/del&gt;-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;notes/trial-result-event-outcome&lt;/del&gt;.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;php | accessdate = 22 July 2013}}&lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;/ref&lt;/del&gt;&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;==Mathematical description==&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{{main|Probability space}}&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;A random experiment is described &lt;/del&gt;or &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;modeled by a mathematical construct known &lt;/del&gt;as a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[probability space]]. A probability space &lt;/del&gt;is &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;constructed and defined &lt;/del&gt;with &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;a specific kind &lt;/del&gt;of &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;experiment or trial in mind&lt;/del&gt;.&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;A mathematical description of an experiment consists of three parts&lt;/del&gt;:&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;# A [[sample space]&lt;/del&gt;], &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Ω (or &#039;&#039;S&#039;&#039;), which is the [[Set (mathematics)|set]] of all possible [[Outcome (probability)|outcomes]]&lt;/del&gt;.&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;# A set of [[Event (probability theory)|event]]s &lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;math&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;\scriptstyle \mathcal{F}&lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;/math&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;, where each event is &lt;/del&gt;a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;set containing zero or more outcomes&lt;/del&gt;.&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;# The assignment of [[probability|probabilities]] to the events&amp;amp;mdash; that &lt;/del&gt;is&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;, &lt;/del&gt;a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;function &#039;&#039;P&#039;&#039; mapping &lt;/del&gt;from &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;events to probabilities.&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;An &#039;&#039;outcome&#039;&#039; is &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;result of a single execution of the model&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Since individual outcomes might be of little practical use&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;more complicated &#039;&#039;events&#039;&#039; &lt;/del&gt;are &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;used to characterize groups of outcomes&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;The collection of all such events is a &#039;&#039;[[sigma-algebra]]&#039;&#039; &lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;math&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;\scriptstyle \mathcal{F}&lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;/math&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;. Finally, there is &lt;/del&gt;a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;need to specify each event&#039;s likelihood of happening; this is done using &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&#039;&#039;&lt;/del&gt;[&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[probability measure&lt;/del&gt;]&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;]&#039;&#039; function&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&#039;&#039;P&#039;&#039;.&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Once an experiment is designed &lt;/del&gt;and &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;established, it is assumed &lt;/del&gt;that &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;“nature” makes its move and selects a single outcome, &#039;&#039;ω&#039;&#039;, from the sample space Ω&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;All the events in &lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;math&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;\scriptstyle \mathcal{F}&lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;/math&lt;/del&gt;&amp;gt; &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;that contain &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;selected outcome &#039;&#039;ω&#039;&#039; (recall that each event is &lt;/del&gt;a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;subset &lt;/del&gt;of &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Ω) are said to “have occurred”. The probability function &#039;&#039;P&#039;&#039; is defined in such &lt;/del&gt;a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;way &lt;/del&gt;that&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;, if &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;experiment were to be repeated an infinite number &lt;/del&gt;of &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;times, &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;relative frequencies of occurrence of each of &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;events would [[Limit (mathematics)|approach]] agreement &lt;/del&gt;with &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;the values &#039;&#039;P&#039;&#039; assigns &lt;/del&gt;them.&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;==See also==&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;* &lt;/del&gt;[&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[Probability space]]&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;References&lt;/del&gt;=&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;=&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{{reflist}}&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Category:Probability theory]&lt;/del&gt;]&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>en&gt;ClueBot NG</name></author>
	</entry>
	<entry>
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		<title>en&gt;Materialscientist: Reverted 1 edit by 207.177.117.19 identified as test/vandalism using STiki</title>
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		<updated>2014-01-07T16:07:34Z</updated>

		<summary type="html">&lt;p&gt;Reverted 1 edit by &lt;a href=&quot;/wiki/Special:Contributions/207.177.117.19&quot; title=&quot;Special:Contributions/207.177.117.19&quot;&gt;207.177.117.19&lt;/a&gt; identified as test/vandalism using &lt;a href=&quot;/index.php?title=WP:STiki&amp;amp;action=edit&amp;amp;redlink=1&quot; class=&quot;new&quot; title=&quot;WP:STiki (page does not exist)&quot;&gt;STiki&lt;/a&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 18:07, 7 January 2014&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot;&gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{{About|probabilistic experiments|a more general discussion|Experiment}}&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{{Probability fundamentals}}&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;In probability theory, an &#039;&#039;&#039;experiment&#039;&#039;&#039; or &#039;&#039;&#039;trial&#039;&#039;&#039; (see below) is any procedure that can be infinitely repeated and has a well-defined [[Set (mathematics)|set]] of possible [[Outcome (probability)|outcomes]], known as the [[sample space]].&amp;lt;ref&amp;gt;{{cite web |url=http://www-math.bgsu.edu/~albert/m115/probability/sample_space.html |title=Listing All Possible Outcomes (The Sample Space) |last=Albert |first=Jim |date=21 January 1998 |publisher= Bowling Green State University |accessdate=June 25, 2013}}&amp;lt;/ref&amp;gt; An experiment is said to be &#039;&#039;random&#039;&#039; if it has more than one possible outcome, and &#039;&#039;deterministic&#039;&#039; if it has only one. A random experiment that has exactly two ([[Mutually exclusive events|mutually exclusive]]) possible outcomes is known as a [[Bernoulli trial]].&amp;lt;ref&amp;gt;{{cite encyclopedia | last = Papoulis | first =  Athanasios | contribution = Bernoulli Trials | title = Probability, Random Variables, and Stochastic Processes | edition =  2nd | url = http://www.mhhe.com/engcs/electrical/papoulis/ | location = New York | publisher = [[McGraw-Hill]] | pages = 57–63 | year = 1984}}&amp;lt;/ref&amp;gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Today&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;there are several other types &lt;/del&gt;of &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;web development and blogging software available &lt;/del&gt;to &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;design and host your website blogs online and &lt;/del&gt;that &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;too in minutes, if not hours&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Thus&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;it is important &lt;/del&gt;to &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;keep pace with this highly advanced age &lt;/del&gt;and &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;have a regular interaction with your audience to keep a strong hold &lt;/del&gt;in the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;business market. 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I have never seen a plugin with &lt;/del&gt;such a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;massive array of features, this does everything &lt;/del&gt;that &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;platinum SEO and All In One SEO&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;also throws in &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;functionality found within SEO Smart Links and a &lt;/del&gt;number of &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;other plugins it is essentially &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;swiss army knife &lt;/del&gt;of &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Word - Press plugins&lt;/del&gt;.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;When an experiment is conducted&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;one (and only one) outcome results&amp;amp;mdash; although this outcome may be included in any number of [[Event (probability theory)|events]], all &lt;/ins&gt;of &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;which would be said &lt;/ins&gt;to &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;have occurred on &lt;/ins&gt;that &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;trial&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;After conducting many trials of the same experiment and pooling the results&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;an experimenter can begin &lt;/ins&gt;to &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;assess the [[Empirical probability|empirical probabilities]] of the various outcomes &lt;/ins&gt;and &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;events that can occur &lt;/ins&gt;in the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;experiment and apply the methods of [[Statistics|statistical analysis]]&lt;/ins&gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;==Experiments &lt;/ins&gt;and &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;trials==&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Random experiments are often conducted repeatedly&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;so &lt;/ins&gt;that the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;collective results may be subjected to [[Statistics|statistical analysis]]. A fixed number &lt;/ins&gt;of &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;repetitions of the same experiment &lt;/ins&gt;can &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;be thought &lt;/ins&gt;of &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;as a &#039;&#039;&#039;composed experiment&#039;&#039;&#039;, in which case &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;individual repetitions are called &#039;&#039;&#039;trials&#039;&#039;&#039;&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;For example, if one were to toss &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;same coin one hundred times and record each result&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;each toss would be considered a trial within the experiment composed of all hundred tosses&lt;/ins&gt;.&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;ref&lt;/ins&gt;&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{{cite web | publisher = Future a/ccountant | title = Trial, Experiment, Event, Result/Outcome | url = http://www.futureaccountant.com/probability/study-notes/trial-result-event-outcome.php | accessdate = 22 July 2013}}&lt;/ins&gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;/ref&lt;/ins&gt;&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;==Mathematical description==&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{{main|Probability space}}&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;A random experiment &lt;/ins&gt;is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;described or modeled by a mathematical construct &lt;/ins&gt;known as &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;a [[probability space]]. A probability space is constructed &lt;/ins&gt;and &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;defined with a specific kind &lt;/ins&gt;of &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;experiment or trial in mind&lt;/ins&gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;A mathematical description of an experiment consists &lt;/ins&gt;of &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;three parts&lt;/ins&gt;:&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;# A [[sample space]], Ω (or &#039;&#039;S&#039;&#039;), which is &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Set (mathematics)|set]] &lt;/ins&gt;of &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;all &lt;/ins&gt;possible &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Outcome (probability)|outcomes]]&lt;/ins&gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;# A set of [[Event (probability theory)|event]]s &lt;/ins&gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;math&lt;/ins&gt;&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;\scriptstyle \mathcal{F}&lt;/ins&gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;/math&lt;/ins&gt;&amp;gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;where each event is &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;set containing zero &lt;/ins&gt;or &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;more outcomes&lt;/ins&gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;# The assignment &lt;/ins&gt;of &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[probability|probabilities]] to &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;events&amp;amp;mdash; that &lt;/ins&gt;is&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;, a function &#039;&#039;P&#039;&#039; mapping from events &lt;/ins&gt;to &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;probabilities&lt;/ins&gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;An &#039;&#039;outcome&#039;&#039; &lt;/ins&gt;is the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;result &lt;/ins&gt;of a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;single execution of the model&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Since individual outcomes might be of little practical use&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;more complicated &#039;&#039;events&#039;&#039; &lt;/ins&gt;are &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;used to characterize groups &lt;/ins&gt;of &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;outcomes&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;The collection of all such events is a &#039;&#039;[&lt;/ins&gt;[&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;sigma-algebra]&lt;/ins&gt;]&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&#039;&#039; &lt;/ins&gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;math&lt;/ins&gt;&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;\scriptstyle \mathcal{F}&lt;/ins&gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;/math&lt;/ins&gt;&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;. Finally&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;there is &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;need to specify each event&#039;s likelihood of happening; this is done using the &#039;&#039;[[probability measure]]&#039;&#039; function&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&#039;&#039;P&#039;&#039;.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Once an experiment is designed &lt;/ins&gt;and &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;established&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;it is assumed that “nature” makes its move &lt;/ins&gt;and &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;selects &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;single outcome, &#039;&#039;ω&#039;&#039;&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;from the sample space Ω&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;All &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;events in &amp;lt;math&amp;gt;\scriptstyle \mathcal{F}&amp;lt;/math&amp;gt; that contain &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;selected outcome &#039;&#039;ω&#039;&#039; (recall &lt;/ins&gt;that &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;each event &lt;/ins&gt;is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;a subset of Ω) are said &lt;/ins&gt;to &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;“have occurred”&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;The probability function &#039;&#039;P&#039;&#039; &lt;/ins&gt;is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;defined &lt;/ins&gt;in such a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;way &lt;/ins&gt;that, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;if &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;experiment were to be repeated an infinite &lt;/ins&gt;number of &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;times, &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;relative frequencies of occurrence of each &lt;/ins&gt;of &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;the events would [[Limit (mathematics)|approach]] agreement with the values &#039;&#039;P&#039;&#039; assigns them&lt;/ins&gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;==See also==&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;* [[Probability space]]&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;==References==&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{{reflist}}&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Category:Probability theory]]&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>en&gt;Materialscientist</name></author>
	</entry>
	<entry>
		<id>https://en.formulasearchengine.com/index.php?title=Isotope&amp;diff=262209&amp;oldid=prev</id>
		<title>en&gt;ClueBot NG: Reverting possible vandalism by 49.145.34.190 to version by DexDor. False positive? Report it. Thanks, ClueBot NG. (1190938) (Bot)</title>
		<link rel="alternate" type="text/html" href="https://en.formulasearchengine.com/index.php?title=Isotope&amp;diff=262209&amp;oldid=prev"/>
		<updated>2012-08-31T09:15:24Z</updated>

		<summary type="html">&lt;p&gt;Reverting possible vandalism by &lt;a href=&quot;/wiki/Special:Contributions/49.145.34.190&quot; title=&quot;Special:Contributions/49.145.34.190&quot;&gt;49.145.34.190&lt;/a&gt; to version by DexDor. False positive? &lt;a href=&quot;/index.php?title=User:ClueBot_NG/FalsePositives&amp;amp;action=edit&amp;amp;redlink=1&quot; class=&quot;new&quot; title=&quot;User:ClueBot NG/FalsePositives (page does not exist)&quot;&gt;Report it&lt;/a&gt;. Thanks, &lt;a href=&quot;/index.php?title=User:ClueBot_NG&amp;amp;action=edit&amp;amp;redlink=1&quot; class=&quot;new&quot; title=&quot;User:ClueBot NG (page does not exist)&quot;&gt;ClueBot NG&lt;/a&gt;. (1190938) (Bot)&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;&lt;br /&gt;
&lt;br /&gt;
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		<author><name>en&gt;ClueBot NG</name></author>
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