(a) Use LOTUS to show that for X Pois(λ) and any function g, This is called the Stein-Chen identity for the Poisson. (b) Find the third moment E(X3) for X ~ Pois(λ) by using the identity from (a)...

This is called the Stein-Chen identity for the Poisson.

(b) Find the third moment E(X³) for X ~ Pois(λ) by using the identity from (a) and a bit of algebra to reduce the calculation to the fact that X has mean and variance .