AP Statistics Curriculum 2007 Limits Poisson2Bin - Revision history

WikiSysop: /* Problems */

2014-07-28T13:44:07Z

‎Problems

WikiSysop: /* Problems */

2014-07-28T13:43:32Z

‎Problems

Dinov: /* Poisson as Approximation to Binomial Distribution */

2014-06-09T18:09:00Z

‎Poisson as Approximation to Binomial Distribution

Jenny at 17:06, 28 June 2010

2010-06-28T17:06:57Z

IvoDinov: added a link to the Problems set

2009-10-26T05:02:33Z

added a link to the Problems set

PriscillaChui: /* General Advance-Placement (AP) Statistics Curriculum - Poisson as Approximation to Binomial Distribution */

2008-03-01T22:19:38Z

‎ General Advance-Placement (AP) Statistics Curriculum - Poisson as Approximation to Binomial Distribution

IvoDinov: /* Examples */

2008-02-03T01:40:02Z

‎Examples

IvoDinov at 01:39, 3 February 2008

2008-02-03T01:39:00Z

IvoDinov at 19:01, 14 June 2007

2007-06-14T19:01:46Z

IvoDinov at 19:00, 14 June 2007

2007-06-14T19:00:36Z

New page

==[[AP_Statistics_Curriculum_2007 | General Advance-Placement (AP) Statistics Curriculum]] - Poisson as Approximation to Binomial Distribution==

=== POisson as Approximation to Binomial Distribution===
Example on how to attach images to Wiki documents in included below (this needs to be replaced by an appropriate figure for this section)!
<center>[[Image:AP_Statistics_Curriculum_2007_IntroVar_Dinov_061407_Fig1.png|500px]]</center>

===Approach===
Models & strategies for solving the problem, data understanding & inference.

* TBD

===Model Validation===
Checking/affirming underlying assumptions.

* TBD

===Computational Resources: Internet-based SOCR Tools===
* TBD

===Examples===
Computer simulations and real observed data.

* TBD

===Hands-on activities===
Step-by-step practice problems.

* TBD

<hr>
===References===
* TBD

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

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 <hr>
-* SOCR Home page: http://www.socr.ucla.edu
+* SOCR Home page: http://www.socr.umich.edu
 {{translate|pageName=http://wiki.socr.umich.edu/index.php?title=AP_Statistics_Curriculum_2007_Limits_Poisson2Bin}}

← Older revision		Revision as of 13:43, 28 July 2014
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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?title=AP_Statistics_Curriculum_2007_Limits_Poisson2Bin}}	+	{{translate\|pageName=http://wiki.socr.umich.edu/index.php?title=AP_Statistics_Curriculum_2007_Limits_Poisson2Bin}}

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 * Note that the conditions of [[AP_Statistics_Curriculum_2007_Distrib_Poisson | Poisson]] approximation to [[AP_Statistics_Curriculum_2007_Distrib_Binomial | Binomial]] are complementary to the [[AP_Statistics_Curriculum_2007_Limits_Norm2Bin | conditions for Normal Approximation of Binomial Distribution]]. Poisson Approximation to Binomial is appropriate when:
-: <math>np < 10</math>
+: \(np < 10\)
 : <math>n \geq 20</math> and <math>p \leq 0.05</math>.
 ===Examples===

@@ Line 4: / Line 4: @@
 The [[AP_Statistics_Curriculum_2007_Distrib_Poisson#Poisson_as_a_limiting_case_of_Binomial_distribution | complete details of the Poisson Distribution as a limiting case of the Binomial Distribution are contained here.]]
-* Note that the conditions of [[AP_Statistics_Curriculum_2007_Distrib_Poisson | Poisson]] approximation to [[AP_Statistics_Curriculum_2007_Distrib_Binomial | Binomial]] are complementary to the [[AP_Statistics_Curriculum_2007_Limits_Norm2Bin | conditions for Normal Approximation of Binomial Distribution]]. Poisson Approximation to Binomial is an appropriate when:
+* Note that the conditions of [[AP_Statistics_Curriculum_2007_Distrib_Poisson | Poisson]] approximation to [[AP_Statistics_Curriculum_2007_Distrib_Binomial | Binomial]] are complementary to the [[AP_Statistics_Curriculum_2007_Limits_Norm2Bin | conditions for Normal Approximation of Binomial Distribution]]. Poisson Approximation to Binomial is appropriate when:
 : <math>np < 10</math>
 : <math>n \geq 20</math> and <math>p \leq 0.05</math>.

@@ Line 2: / Line 2: @@
 === Poisson as Approximation to Binomial Distribution===
-The [[AP_Statistics_Curriculum_2007_Distrib_Poisson#Poisson_as_a_limiting_case_of_Binomial_distribution | complete details of the Poisson Distribution as a limiting case of the Binomial Distirbution are contained here.]]
+The [[AP_Statistics_Curriculum_2007_Distrib_Poisson#Poisson_as_a_limiting_case_of_Binomial_distribution | complete details of the Poisson Distribution as a limiting case of the Binomial Distribution are contained here.]]
 * Note that the conditions of [[AP_Statistics_Curriculum_2007_Distrib_Poisson | Poisson]] approximation to [[AP_Statistics_Curriculum_2007_Distrib_Binomial | Binomial]] are complementary to the [[AP_Statistics_Curriculum_2007_Limits_Norm2Bin | conditions for Normal Approximation of Binomial Distribution]]. Poisson Approximation to Binomial is an appropriate when:
@@ Line 20: / Line 20: @@
 <hr>
-===References===
+===[[EBook_Problems_Limits_Poisson2Bin|Problems]]===
 <hr>

@@ Line 9: / Line 9: @@
 ===Examples===
-The [[About_pages_for_SOCR_Distributions | Binomial distribution]] can be approximated well by Poisson when <math> n </math> is large and <math> p </math> is small with <math> np < 7 </math>.  This is true because
+The [[About_pages_for_SOCR_Distributions | Binomial distribution]] can be approximated well by Poisson when <math> n </math> is large and <math> p </math> is small with <math> np < 10 </math>, as stated above.  This is true because
 <math> \lim_{n \rightarrow \infty}
 {n \choose x} p^x(1-p)^{n-x}=\frac{\lambda^x e^{-\lambda}}{x!} </math>, where
@@ Line 19: / Line 19: @@
 <hr>
 ===References===

@@ Line 2: / Line 2: @@
 === Poisson as Approximation to Binomial Distribution===
-Example on how to attach images to Wiki documents in included below (this needs to be replaced by an appropriate figure for this section)!
+The [[AP_Statistics_Curriculum_2007_Distrib_Poisson#Poisson_as_a_limiting_case_of_Binomial_distribution | complete details of the Poisson distribution as a limiting case of the Binomial Distirbution are contained here.]]
-===Approach===
+* Note that the conditions of [[AP_Statistics_Curriculum_2007_Distrib_Poisson | Poisson]] approximation to [[AP_Statistics_Curriculum_2007_Distrib_Binomial | Binomial]] are complementary to the [[AP_Statistics_Curriculum_2007_Limits_Norm2Bin | conditions for Normal approximation of Binomial distribution]]. Poisson approximation to Binomial is an appropriate when:
-Models & strategies for solving the problem, data understanding & inference.
+: <math>np < 10</math>
+: <math>n \geq 20</math> and <math>p \leq 0.05</math>.
 ===Examples===
-Computer simulations and real observed data.
+The [[About_pages_for_SOCR_Distributions | Binomial distribution]] can be approximated well by Poisson when <math> n </math> is large and <math> p </math> is small with <math> np < 7 </math>.  This is true because
+<math> \lim_{n \rightarrow \infty}
-* TBD
+{n \choose x} p^x(1-p)^{n-x}=\frac{\lambda^x e^{-\lambda}}{x!} </math>, where
+<math> \lambda=np </math>.  Here is an example.  Suppose <math> 2\% </math> of a certain population have Type AB blood.  Suppose 60 people from this population are randomly selected.  The number of people <math> X </math> among the 60 that have Type AB blood follows the Binomial distribution with <math> n=60, p=0.02 </math>.  The figure below represents the distribution of <math> X </math>.  This figure also shows <math> P(X=0) </math>.
-===Hands-on activities===
+<center>[[Image: SOCR_Activities_ExploreDistributions_Christou_figure13.jpg|600px]]</center>
-* TBD
+* '''Note''': This distribution can be approximated well with Poisson with <math> \lambda=np=60(0.02)=1.2 </math>.  The figure below is approximately the same as the figure above (the width of the bars is not important here.  The height of each bar represents the probability for each value of <math> X </math> which is about the same for both distributions).
 <hr>
 ===References===
 <hr>

@@ Line 1: / Line 1: @@
 ==[[AP_Statistics_Curriculum_2007 | General Advance-Placement (AP) Statistics Curriculum]] - Poisson as Approximation to Binomial Distribution==
-=== POisson as Approximation to Binomial Distribution===
+=== Poisson as Approximation to Binomial Distribution===
 Example on how to attach images to Wiki documents in included below (this needs to be replaced by an appropriate figure for this section)!
 <center>[[Image:AP_Statistics_Curriculum_2007_IntroVar_Dinov_061407_Fig1.png|500px]]</center>