Question

泊松分布的一道题目

Let X be a poisson random variable with mean equal to 10.find E[X^2]
该如何求??

Answer 1

http://baike.baidu.com/view/79815.htm

For Poisson variable X, we know that E{X}=λ and Var{X}=λ too.
Therefore, E{X^2} = Var{X}+(E{X})^2 = 10+10^2 = 110.

Answer 2

For poisson distribution, E[X] = Var[X]

Var[X] = E[X^2] - E^2[X] => E[X^2] = Var[X] + E^2[X] = E[X] + E^2[X] = 100