# How do you determine the variance of a Poisson distribution?

##### 1 Answer

Nov 8, 2015

The Poisson Distribution is that of a discrete random variable. Hence we use the summation procedure.

#### Explanation:

For any random variable X, the variance is defined as

#sigma^2# = E(#X^2# ) -# [E(X)]^2# .

if the random variable is a discrete random variable, we obtain

#sigma^2# =#sum_0^infty# #x^2# p(x) -# [ sum_0^inftyx.p(x)]^2# where

p(x) =#((e^(-mu}mu^x) / (x!)) # x = 0,1,2,3,-----#infty#

Finally, the answer is obtained as#mu# .