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 * [[CP_May2007_Name_Context_Date  This is just an Example Wiki Page]] (the title of this Wiki page is [[CP_May2007_Name_Context_Date]]  use the same syntax to create your own page)   * [[CP_May2007_Name_Context_Date  This is just an Example Wiki Page]] (the title of this Wiki page is [[CP_May2007_Name_Context_Date]]  use the same syntax to create your own page) 
   
 
 
 
 
 
 
 
 
 
 
  == This is an activity to explore the Binomial, Geometric, and Hypergeometric Probability Distributions.==
 
 
 
  * '''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:
 
  **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.
 
  **b. <math> X \sim b(10,0.1) </math>, find <math> P(1 \le X \le 3) </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>.
 
  **d. <math> X \sim b(30,0.1) </math>, find <math> P(X > 2) </math>.
 
 
 
  Below you can see a snapshot of the distribution of <math> X \sim b(20,0.3) </math>
 
 
 
 
 
  <center>[[Image: SOCR_Activities_Binomial_Christou__binomial.jpg600px]]</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.jpg600px]]</center>
 
 
 
  <math>\sqrt(n)</math>
 
 
 
  * '''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 3 agree with the formulas discussed in class, for example, <math> P(X=x)=(1p)^{x1}p </math>, <math> P(X > k)=(1p)^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.jpg600px]]</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.
 
 
 
  * '''Exercise 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 exercise 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.
 
 
 
 
 
  <hr>
 
  * SOCR Home page: http://www.socr.ucla.edu
 
 
 
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  <hr>
 
  * [http://wiki.stat.ucla.edu/socr/index.php/SOCR_Events_May2007 Back to the SOCR USCOTS 2007 Breakout session]
 
  * [http://wiki.stat.ucla.edu/socr/uploads/d/d5/SOCR_CAUSEwayWorkshopFlier_Apr2007.pdf SOCR/CAUSEway Workshop Flier] ([[SOCR_Events_Aug2007  Aug. 0608, 2007, UCLA]])
 
  * [[SOCR_EduMaterials_GuidelinesWikiEditing  SOCR Wiki Resource Editing Guide]]
 
  * SOCR Home page: http://www.socr.ucla.edu
 
   
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