# Poisson Distribution

1. Sep 21, 2010

### rhyno89

1. The problem statement, all variables and given/known data
We can approximate a poisson distribution from the normal. Suppose lambda is a large positive value; let X ~ Poisson(lambda) and let X1.....Xn be independant identicly distributed from a Poisson (lambda/n) distribution. Then X and X1+....+Xn have the same distribution. Use the central limit theorem to determine the approximate distribution of X.......

2. Relevant equations

3. The attempt at a solution

I know that the above statement is true through moment generating functions. If X is distributed with mean of lambda then n random variables with a mean of lambda over n will sum to a distribution with mean of lambda.

It seems from the question that the distribution of X would just be a poisson distribution with mean of lambda but that doesnt really require any work as the problem states that.

Any help on getting started?