# Homework Help: Negative Binomial random variable

1. Sep 26, 2011

### sam_0017

Data is collected on the number of fish caught per day on a month long fishing expedition. It is hypothesised that the data are consistent with a negative Binomial random variable ,X , starting at 0, so that X~Neg Bin(k,p) where E[X]=k(1-p)/p and Var =k(1-p)/p^2 . However, before a hypothesis test can be performed, estimates of k and p (denoted by Kand P, respectively) are required. Show how you can obtain K and P based on the sample mean x` and sample variance s^2 of the fishing data.

2. Oct 3, 2011

### Eynstone

Re: Challenge !!

E[X]/Var = p and k=pE[X]/(1-p).