# SOCR EduMaterials Activities NegativeBinomial Distributions

## This is an activity to explore the Negative 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. \( X \) follows the negative binomial distribution with \( r=5, \ p=0.2 \).
- b. \( X \) follows the negative binomial distribution with \( r=5, \ p=0.9 \).
- c. \( X \) follows the negative binomial distribution with \( r=20, \ p=0.3 \).
- d. \( X \) follows the negative binomial distribution with \( r=20, \ p=0.9 \).

**Exercise 2:**Let \( X \) follows the negative binomial distribution with \( r=5, \ p=0.2 \). Explain in words what \( P(X > 10) \) means and use SOCR to compute this probability.

Below you can see the distribution of negative binomial with \( r=15, \ p=0.8 \). In this graph you can also see the probability that the 5th success occurs on the 18th or 19th or 20th or 21st or 22nd trial.

- SOCR Home page: http://www.socr.ucla.edu

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