# SOCR EduMaterials Activities NegativeBinomial Distributions

## This is an activity to explore the Negative Binomial Probability Distribution.

• 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.