Difference between revisions of "SOCR EduMaterials Activities Discrete Distributions"

Revision as of 17:54, 27 October 2006

This is an activity to explore the Negaive Binomial Probability Distribution.

Description: You can access the applets for the above distributions at http://www.socr.ucla.edu/htmls/SOCR_Distributions.html .

Exercise 1: Use SOCR to graph and print the following distributions and comment on the shape of each one of them:
- a. \( X <\math> follows negative binomial with <math> r=5, \ p=0.2 <\math>. ** b. <math> X <\math> follows negative binomial with <math> r=5, \ p=0.9 <\math>. ** c. <math> X <\math> follows negative binomial with <math> r=20, \ p=0.3 <\math>. ** d. <math> X <\math> follows negative binomial with <math> r=20, \ p=0.9 <\math>. * '''Exercise 2:''' Let <math> X <\math> follows the negative binomial distribution with <math> r=5, \ p=0.2 <\math>. Explain in words what <math> P(X > 10) <\math> means and use SOCR to compute this probability. Below you can see the distribution of <math> X \sim b(20,0.3) <\math> <center>[[Image: SOCR_Activities_Christou_negbinomial.jpg|600px]]</center> <hr> * SOCR Home page: http://www.socr.ucla.edu ----- ----- Translate this page: <center> {| style="text-align: left; width: 535px; height: 226px" cellspacing="2" cellpadding="2" | style="text-align: center; vertical-align: middle" | [http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_ConfidenceIntervals '''(default)'''] [[image:uk_flag.gif|15px]] | style="text-align: center; vertical-align: middle" | [https://wiki-socr-umich-edu.translate.goog/index.php/SOCR_EduMaterials_Activities_Discrete_Distributions?_x_tr_sl=auto&_x_tr_tl=de '''Deutsch'''] [[image:de_flag.gif|15px]] | style="text-align: center; vertical-align: middle" | [https://wiki-socr-umich-edu.translate.goog/index.php/SOCR_EduMaterials_Activities_Discrete_Distributions?_x_tr_sl=auto&_x_tr_tl=es '''Español'''] [[image:es_flag.gif|15px]] | style="text-align: center; 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vertical-align: middle" | [https://wiki-socr-umich-edu.translate.goog/index.php/SOCR_EduMaterials_Activities_Discrete_Distributions?_x_tr_sl=auto&_x_tr_tl=hr '''Hrvatska'''] [[image:hr_flag.gif|15px]] | style="text-align: center; vertical-align: middle" | [https://wiki-socr-umich-edu.translate.goog/index.php/SOCR_EduMaterials_Activities_Discrete_Distributions?_x_tr_sl=auto&_x_tr_tl=cs '''Česká republika'''] [[image:cz_flag.gif|15px]] | style="text-align: center; vertical-align: middle" | [https://wiki-socr-umich-edu.translate.goog/index.php/SOCR_EduMaterials_Activities_Discrete_Distributions?_x_tr_sl=auto&_x_tr_tl=da '''Danmark'''] [[image:dk_flag.gif|15px]] | style="text-align: center; vertical-align: middle" | [https://wiki-socr-umich-edu.translate.goog/index.php/SOCR_EduMaterials_Activities_Discrete_Distributions?_x_tr_sl=auto&_x_tr_tl=pl '''Polska'''] [[image:pl_flag.png|15px]] | style="text-align: center; vertical-align: middle" | [https://wiki-socr-umich-edu.translate.goog/index.php/SOCR_EduMaterials_Activities_Discrete_Distributions?_x_tr_sl=auto&_x_tr_tl=ro '''România'''] [[image:ro_flag.png|15px]] | style="text-align: center; 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@@ Line 1: / Line 1: @@
-== This is an activity to explore the Binomial, Geometric, and Hypergeometric Probability Distributions.==
+== This is an activity to explore the Negaive Binomial Probability Distribution.==
 * '''Description''':  You can access the applets for the above distributions at  http://www.socr.ucla.edu/htmls/SOCR_Distributions.html .
-* '''Exercise 1:''' Use SOCR to graph and print the following distributions and answer the questions below.  Also, comment on the shape of each one of these distributions:
+* '''Exercise 1:''' Use SOCR to graph and print the following distributions and comment on the shape of each one of them:
-**a. <math> X \sim b(10,0.5) </math>, find <math> P(X=3) </math>, <math> E(X) </math>, <math> sd(X) </math>, and verify them with the formulas discussed in class.
+** a. <math> X <\math> follows negative binomial with <math> r=5, \ p=0.2 <\math>.
-**b. <math> X \sim b(10,0.1) </math>,  find <math> P(1 \le X \le 3) </math>.
+** b. <math> X <\math> follows negative binomial with <math> r=5, \ p=0.9 <\math>.
-**c. <math> X \sim b(10,0.9) </math>, find <math> P(5 < X < 8), \ P(X < 8), \ P(X \le 7), \ P(X \ge 9) </math>.
+** c. <math> X <\math> follows negative binomial with <math> r=20, \ p=0.3 <\math>.
-**d. <math> X \sim b(30,0.1) </math>, find <math> P(X > 2) </math>.
+** d. <math> X <\math> follows negative binomial with <math> r=20, \ p=0.9 <\math>.
+* '''Exercise 2:''' Let <math> X <\math>  follows the negative binomial distribution with <math> r=5, \ p=0.2 <\math>.  Explain in words what <math> P(X > 10) <\math> means and use SOCR to compute this probability.
-Below you can see a snapshot of the distribution of <math> X \sim b(20,0.3) </math>
+Below you can see the distribution of <math> X \sim b(20,0.3) <\math>
-<center>[[Image: SOCR_Activities_Binomial_Christou__binomial.jpg|600px]]</center>
+<center>[[Image: SOCR_Activities_Christou_negbinomial.jpg|600px]]</center>
-* '''Exercise 2:''' Use SOCR to graph and print the distribution of a geometric random variable with <math> p=0.2,  p=0.7 </math>.  What is the shape of these distributions?  What happens when <math> p </math> is large?  What happens when <math> p </math> is small?
-Below you can see a snapshot of the distribution of <math> X \sim geometric(0.4) </math>
-<center>[[Image: SOCR_Activities_Christou_geometric.jpg|600px]]</center>
-* '''Exercise 3:''' Select the geometric probability distribution with <math> p=0.2 </math>.  Use SOCR to compute the following:
-**a. <math> P(X=5) </math>
-**b. <math> P(X > 3) </math>
-**c. <math> P(X \le 5) </math>
-**d. <math> P(X > 6) </math>
-**e. <math> P(X \ge 8) </math>
-**f. <math> P(4 \le X \le 9) </math>
-**g. <math> P(4 < X < 9) </math>
-* '''Exercise 4:''' Verify that your answers in exercise 3agree with the formulas discussed in class, for example, <math> P(X=x)=(1-p)^{x-1}p </math>, <math> P(X > k)=(1-p)^k </math>, etc.  Write all your answers in detail using those formulas.
-* '''Exercise 5:''' Let <math> X </math> follow the hypergeometric probability distribution with <math> N=52 </math>, <math> n=10 </math>, and number of "hot" items 13.  Use SOCR to graph and print this distribution.
-Below you can see a snapshot of the distribution of <math> X \sim hypergeometric(N=100, n=15, r=30) </math>
-<center>[[Image: SOCR_Activities_Christou_hypergeometric.jpg|600px]]</center>
-* '''Exercise 6:''' Refer to exercise 5.  Use SOCR to compute <math> P(X=5) </math> and write down the formula that gives this answer.
-* '''Exericise 7:''' Binomial approximation to hypergeometric:  Let <math> X </math> follow the hypergeometric probability distribution with <math> N=1000, \ n=10 </math> and number of "hot" items 50.  Graph and print this distribution.
-* '''Exercise 8:''' Refer to exerciise 7.  Use SOCR to compute the exact probability: <math> P(X=2) </math>.  Approximate <math> P(X=2) </math> using the binomial distribution.  Is the approximation good?  Why?
-* '''Exercise 9:''' Do you think you can approximate well the hypergeometric probability distribution with <math> N=50, \ n=10 </math>, and number of "hot" items 40 using the binomial probability distribution?  Explain.
@@ Line 55: / Line 23: @@
 {{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_ConfidenceIntervals}}
+</math>

Difference between revisions of "SOCR EduMaterials Activities Discrete Distributions"

Revision as of 17:54, 27 October 2006

This is an activity to explore the Negaive Binomial Probability Distribution.

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