SOCR EduMaterials Activities Discrete Distributions
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(Difference between revisions)
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* '''Exercise 3:''' Select the geometric probability distribution with <math> p=0.2 </math>. Use SOCR to compute the following: | * '''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> | + | a. <math> P(X=5) </math> \\ |
| - | b. <math> P(X > 3) </math> | + | b. <math> P(X > 3) </math> \\ |
c. <math> P(X \le 5) </math> | c. <math> P(X \le 5) </math> | ||
d. <math> P(X > 6) </math> | d. <math> P(X > 6) </math> | ||
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* '''Exericise 7:''' Binomial approximation to hypergeometric: | * '''Exericise 7:''' Binomial approximation to hypergeometric: | ||
| - | Let <math> X </math> follow the hypergeometric probability distribution with <math> N=1000, n=10 < | + | 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 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? | ||
Revision as of 02:49, 22 October 2006
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.
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 3agree with the formulas we discussed in class, for example, P(X = x) = (1 − p)x − 1p, 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.
- Exericise 7: Binomial approximation to hypergeometric:
Let X follow the hypergeometric probability distribution with N = 1000,n = 10 and number of "hot" items 50. Graph and print this distribution.
- Exercise 8: Refer to exerciise 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 N = 50,n = 10, and number of "hot" items 40 using the binomial probability distribution? Explain.
- SOCR Home page: http://www.socr.ucla.edu
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