SOCR CommunityPortal Events May2007
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+ | == 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> | ||
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+ | <center>[[Image: SOCR_Activities_Binomial_Christou__binomial.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? | ||
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+ | Below you can see a snapshot of the distribution of <math> X \sim geometric(0.4) </math> | ||
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+ | |||
+ | <center>[[Image: SOCR_Activities_Christou_geometric.jpg|600px]]</center> | ||
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+ | <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)=(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. | ||
+ | |||
+ | * '''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 | ||
+ | |||
+ | {{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_CommunityPortal_Events_May2007}} | ||
Revision as of 20:13, 18 May 2007
SOCR Events-Specific Community Pages SOCR/USCOTS May 2007 Pages
Please try to keep these pages as clean and hierarchically organized as possible. Refer to the SOCR Editing Guide before you begin contributing to these resources.
- 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. , find P(X = 3), E(X), sd(X), and verify them with the formulas discussed in class.
- b. , find .
- c. , find .
- d. , find P(X > 2).
Below you can see a snapshot of the distribution of
- Exercise 2: Use SOCR to graph and print the distribution of a geometric random variable with p = 0.2,p = 0.7. What is the shape of these distributions? What happens when p is large? What happens when p is small?
Below you can see a snapshot of the distribution of
- Exercise 3: Select the geometric probability distribution with p = 0.2. Use SOCR to compute the following:
- a. P(X = 5)
- b. P(X > 3)
- c.
- d. P(X > 6)
- e.
- f.
- g. P(4 < X < 9)
- Exercise 4: Verify that your answers in exercise 3 agree with the formulas discussed in class, for example, P(X = x) = (1 − p)^{x − 1}p, P(X > k) = (1 − p)^{k}, etc. Write all your answers in detail using those formulas.
- Exercise 5: Let X follow the hypergeometric probability distribution with N = 52, n = 10, and number of "hot" items 13. Use SOCR to graph and print this distribution.
Below you can see a snapshot of the distribution of
- Exercise 6: Refer to exercise 5. Use SOCR to compute P(X = 5) and write down the formula that gives this answer.
- Exercise 7: Binomial approximation to hypergeometric: Let X follow the hypergeometric probability distribution with and number of "hot" items 50. Graph and print this distribution.
- Exercise 8: Refer to exercise 7. Use SOCR to compute the exact probability: P(X = 2). Approximate P(X = 2) using the binomial distribution. Is the approximation good? Why?
- Exercise 9: Do you think you can approximate well the hypergeometric probability distribution with , and number of "hot" items 40 using the binomial probability distribution? Explain.
- SOCR Home page: http://www.socr.ucla.edu
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- Back to the SOCR USCOTS 2007 Breakout session
- SOCR/CAUSEway Workshop Flier ( Aug. 06-08, 2007, UCLA)
- SOCR Wiki Resource Editing Guide
- SOCR Home page: http://www.socr.ucla.edu
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