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?

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

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.