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# .
