AP Statistics Curriculum 2007 Beta - Revision history

WikiSysop at 10:51, 4 April 2023

2023-04-04T10:51:52Z

2023-04-04T10:49:29Z

2020-03-03T18:01:49Z

Text replacement - "{{translate|pageName=http://wiki.stat.ucla.edu/socr/" to ""{{translate|pageName=http://wiki.socr.umich.edu/"

2011-07-18T22:41:58Z

2011-07-18T22:41:49Z

2011-07-11T21:25:44Z

‎Beta Distribution

2011-07-11T21:25:15Z

‎Beta Distribution

2011-07-11T21:10:26Z

‎Applications

2011-07-11T21:01:47Z

‎Example

2011-07-11T21:01:05Z

‎Beta Distribution

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−	~~Ссылка на [https://onion.bs2web-mp.com blacksprut com] - зеркало на блекспрут маркетплейс~~

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		+	Ссылка на [https://onion.bs2web-mp.com blacksprut com] - зеркало на блекспрут маркетплейс

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	* SOCR Home page: http://www.socr.ucla.edu		* SOCR Home page: http://www.socr.ucla.edu

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	* SOCR Home page: http://www.socr.ucla.edu		* SOCR Home page: http://www.socr.ucla.edu

−	{{translate\|pageName=http://wiki.stat.ucla.edu/socr/index.php/~~AP_Statistics_Curriculum_2007_Chi-Square~~}}	+	{{translate\|pageName=http://wiki.stat.ucla.edu/socr/index.php/AP_Statistics_Curriculum_2007_Beta}}

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 ===Beta Distribution===
 '''Definition''': Beta distribution is a distribution that models events which are constrained to take place within an interval defined by a minimum and maximum value.
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 The figure below shows this result using [http://socr.ucla.edu/htmls/dist/Beta_Distribution.html SOCR distributions]
 <center>[[Image:Beta.jpg|600px]]</center>

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 *<font size="3"><math>\alpha</math></font> is a positive shape parameter
 *<font size="3"><math>\beta</math></font> is a positive shape parameter
-*<math>\textstyle\Beta(\alpha,\beta)=\int_0^1 t^{\alpha-1}(1-t)^{\beta-1}dt</math> or <br />
+*<math>\textstyle\Beta(\alpha,\beta)=\int_0^1 t^{\alpha-1}(1-t)^{\beta-1}dt</math> or <br /><math>\textstyle\Beta(\alpha,\beta)=\frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)}</math>, where <math>\Gamma(k)!=(k-1)!=1 \times 2 \times\ 3 \times\cdots \times (k-1)</math>
 *x is a random variable

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 *The time it takes to complete a task
 *The proportion of defective items in a shipment
 ===Example===

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 ===Example===
-Suppose that DVDs in a certain shipment are defective with a Beta distribution with α=2 and β=5. Compute the probability that the shipment has 20% to 30% defective DVDs.
+Suppose that DVDs in a certain shipment are defective with a Beta distribution with <font size="3"><math>\alpha=2</math></font> and <font size="3"><math>\beta=5</math></font>. Compute the probability that the shipment has 20% to 30% defective DVDs.
 We can compute this as follows:

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 where
-*<math>\Beta_x(\alpha,\beta)=\int_0^x t^{\alpha-1}(1-t)^{\beta-1}dt</math>
+*<math>\textstyle\Beta_x(\alpha,\beta)=\int_0^x t^{\alpha-1}(1-t)^{\beta-1}dt</math>
-*<math>\Beta(\alpha,\beta)=\int_0^1 t^{\alpha-1}(1-t)^{\beta-1}dt</math>
+*<math>\textstyle\Beta(\alpha,\beta)=\int_0^1 t^{\alpha-1}(1-t)^{\beta-1}dt</math>
 <br />'''Moment generating function''': The Beta moment-generating function is