Introduction to Probability · Problem 5.1.44

Distributions and Densities — Grinstead & Snell

Mathematics — Probability · hypergeometric-distribution

Problem

Suppose that in the hypergeometric distribution, we let

N

and

k

tend to

\infty

in such a way that the ratio

k/N

approaches a real number

p

between 0 and 1. Show that the hypergeometric distribution tends to the binomial distribution with parameters

n

and

p