STAT 302 Chapter Notes - Chapter 4: Random Variable, Negative Binomial Distribution
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So a negative binomial random variable is in many ways like a geometric variable. In a geometric variable, you try to find the probability of getting your first success after a set number of failures. In a negative binomial, you try to find the probability of getting r success in a number of trails. These trails are bernoulli trails so they are independent and there are only two options, p and q. The difference between a binomial random variable and a negative binomial, is crucial however. In binomial, you calculate the success in n trails. In negative binomial, you calculate the number of trails, it needs to get r successes. So the derivation of the formulae is a little interesting. So we are looking for r successes, so like the probability of obtaining four 2"s when you roll a die.
