Statistical Sciences 2141A/B Lecture Notes - Lecture 16: Negative Binomial Distribution, Bernoulli Trial, Geometric Distribution

• School: Western University
• Department: Statistical Sciences
• Course: Statistical Sciences 2141A/B
• Professor: Joe Raaymakers

Document Summary

So we"re looking at random variables that are interesting when an independent sequence of. Last time we looked at the number of successes. Now, let"s look at the number of trials performed until the first success happens. Or the number of trials until a certain success #r happens. A sequence of independent bernoulli trials where the experiment continues until a total of r successes have been observed, where r is a positive integer. Such that each trial has a constant probability of success p(success on trial i) = p. A negative binomial random variable x is an rv associated with a sequence of bernoulli trials where x is the number of trials until the rth success occurs and p is the probability of success in each trial. The parameters of the distribution are p and r (aka these are what make this family of distributions a family)