AP Statistics Curriculum 2007 Limits Bin2HyperG - Revision history

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

2020-03-03T19:45:38Z

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

Jenny: /* Examples */

2010-06-28T20:22:49Z

‎Examples

IvoDinov: /* Binomial Approximation to HyperGeometric Distribution */

2010-01-31T23:23:51Z

‎Binomial Approximation to HyperGeometric Distribution

IvoDinov: added a link to the Problems set

2009-10-26T05:03:08Z

added a link to the Problems set

PriscillaChui: /* Binomial Approximation to HyperGeometric Distribution */

2008-03-01T22:20:13Z

‎Binomial Approximation to HyperGeometric Distribution

IvoDinov: /* References */

2008-02-03T01:47:51Z

‎References

IvoDinov at 01:47, 3 February 2008

2008-02-03T01:47:10Z

IvoDinov at 19:01, 14 June 2007

2007-06-14T19:01:21Z

New page

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

=== Binomial Approximation to HyperGeometric 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

{{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=AP_Statistics_Curriculum_2007_Limits_Bin2HyperG}}

← Older revision		Revision as of 19:45, 3 March 2020
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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_Bin2HyperG}}	+	"{{translate\|pageName=http://wiki.socr.umich.edu/index.php?title=AP_Statistics_Curriculum_2007_Limits_Bin2HyperG}}

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 <center>[[Image: SOCR_Activities_ExploreDistributions_Christou_figure3.jpg|600px]]</center>
-We will approximate the probability of obtaining 1 green marble using Binomial as follows.  Select the SOCR Binomial distribution and choose number of trials 2 and probablity of success <math> p=\frac{35}{50}=0.7 </math>.  Compare the figure below with the figure above.  They are almost the same!  Why?  Using the Binomial formula we can compute the approximate probability of observing 1 green marble as <math> P(X=1)={2 \choose 1}0.70^10.30^1=0.42 </math> (very close to the exact probability, <b>0.4286</b>).
+We will approximate the probability of obtaining 1 green marble using Binomial as follows.  Select the SOCR Binomial distribution and choose number of trials 2 and probability of success <math> p=\frac{35}{50}=0.7 </math>.  Compare the figure below with the figure above.  They are almost the same!  Why?  Using the Binomial formula we can compute the approximate probability of observing 1 green marble as <math> P(X=1)={2 \choose 1}0.70^10.30^1=0.42 </math> (very close to the exact probability, <b>0.4286</b>).
 <center>[[Image: SOCR_Activities_ExploreDistributions_Christou_figure4.jpg|600px]]</center>
 <hr>
 ===[[EBook_Problems_Limits_Bin2HyperG |Problems]]===

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 *If <math>n=1</math> then <math>X</math> has a [[AP_Statistics_Curriculum_2007_Distrib_Binomial  | Bernoulli distribution]] with parameter <math>p</math>.
-*If <math>N</math> and <math>m</math> are large compared to <math>n</math> and <math>p</math> is not close to 0 or 1, then <math>P(X \le x) \approx P(Y \le x)</math>, where <math>Y</math> has a [[AP_Statistics_Curriculum_2007_Distrib_Binomial  | Binomial(<math>n</math>, <math>p</math>) Distribution]].
+*If <math>N</math> and <math>m</math> are large compared to <math>n</math>, and <math>p</math> is not close to 0 or 1, then <math>P(X \le x) \approx P(Y \le x)</math>, where <math>Y</math> has a [[AP_Statistics_Curriculum_2007_Distrib_Binomial  | Binomial(<math>n</math>, <math>p</math>) Distribution]].
 ===Examples===

@@ Line 21: / Line 21: @@
 <hr>
-===References===
+===[[EBook_Problems_Limits_Bin2HyperG |Problems]]===
 <hr>

@@ Line 6: / Line 6: @@
 *If <math>n=1</math> then <math>X</math> has a [[AP_Statistics_Curriculum_2007_Distrib_Binomial  | Bernoulli distribution]] with parameter <math>p</math>.
-*If <math>N</math> and <math>m</math> are large compared to <math>n</math> and <math>p</math> is not close to 0 or 1, then <math>P(X \le x) \approx P(Y \le x)</math>, where <math>Y</math> has a [[AP_Statistics_Curriculum_2007_Distrib_Binomial  | Binomial(<math>n</math>, <math>p</math>) distribution]].
+*If <math>N</math> and <math>m</math> are large compared to <math>n</math> and <math>p</math> is not close to 0 or 1, then <math>P(X \le x) \approx P(Y \le x)</math>, where <math>Y</math> has a [[AP_Statistics_Curriculum_2007_Distrib_Binomial  | Binomial(<math>n</math>, <math>p</math>) Distribution]].
 ===Examples===

@@ Line 2: / Line 2: @@
 === Binomial Approximation to HyperGeometric 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)!
+Suppose [[AP_Statistics_Curriculum_2007_Distrib_Dists | <math>X \sim Hypergeometric(m, N, n)</math>]] and <math>p=m/N</math>.
-===Approach===
+*If <math>n=1</math> then <math>X</math> has a [[AP_Statistics_Curriculum_2007_Distrib_Binomial  | Bernoulli distribution]] with parameter <math>p</math>.
-* TBD
+*If <math>N</math> and <math>m</math> are large compared to <math>n</math> and <math>p</math> is not close to 0 or 1, then <math>P(X \le x) \approx P(Y \le x)</math>, where <math>Y</math> has a [[AP_Statistics_Curriculum_2007_Distrib_Binomial  | Binomial(<math>n</math>, <math>p</math>) distribution]].
 ===Examples===
-Computer simulations and real observed data.
+An urn contains 50 marbles (35 green and 15 white).  Fifteen marbles are selected without replacement.  Find the probability that exactly 10 out of the 15 selected are green marbles.  The answer to this question can be found using the formula:
-* TBD
+Now, select without replacement only 2 marbles.  Compute the exact probability that 1 green marble is obtained.  This is equal to
+<math> P(X=1)=\frac{{35 \choose 1}{15 \choose 1}}{{50 \choose 2}}=0.4286. </math>  This is also shown on the figure below.
-===Hands-on activities===
+<center>[[Image: SOCR_Activities_ExploreDistributions_Christou_figure3.jpg|600px]]</center>
-* TBD
+We will approximate the probability of obtaining 1 green marble using Binomial as follows.  Select the SOCR Binomial distribution and choose number of trials 2 and probablity of success <math> p=\frac{35}{50}=0.7 </math>.  Compare the figure below with the figure above.  They are almost the same!  Why?  Using the Binomial formula we can compute the approximate probability of observing 1 green marble as <math> P(X=1)={2 \choose 1}0.70^10.30^1=0.42 </math> (very close to the exact probability, <b>0.4286</b>).
 <hr>