# Category Archives: hypergeometric distribution

## Variance of binomial vs. hypergeometric

Given $$N$$ balls of which $$r$$ of them are red and the rest are green. Denote $$X$$ as the number of red balls drawn when sampling with replacement and $$Y$$ as the number of red balls drawn when sampling without replacement.

1. What is the difference between the variance of $$X$$ and the variance of $$Y$$ ?
2. For what values of $$N,n,r$$ is the variance the largest ?

## Mark-recapture

A common problem in ecology, social networks, and marketing is estimating the population of a particular species or type. The mark-recapture method is a classic approach to estimating the population.

Assume we want to estimate the population of sturgeon in a section of the Hudson river. We use the following procedure:

1. Capture and mark $$h$$ sturgeons
2. Recapture $$n$$ sturgeon and you find that $$y$$ of them are marked
3. The estimated sturgeon population is $$N = \frac{h n}{y}$$.

Motivate statement $$3$$ using the hypergeometric distribution.