# Approximating a Binomial Random Variable Using A Poisson Random Variable

A random variable X, taking on values 0,1,2,… is said to be a Poisson random variable with parameter lambda if for some lambda >0,

A commonly known (or maybe not commonly known, depending on who you are) property of a Poisson random variable is that it can be used to approximate a Binomial random variable when n is large and p is small. The following is the derivation of why this is mathematical true:

First, lets set:

Now, for a large n and small p

Hence for large n and small p