Exercise 4.32. The nth factorial moment of a random variable Y is defined as the expectation E[Y(Y −1)···(Y −n+1)]. (a) Suppose that Y ∼ Poisson(μ). Find an exact expression for the nth factorial moment of Y . Hint. Use a similar argument as the one used in the proof of Fact 4.18. (b) Compute the third moment E(Y 3) of Y ∼ Poisson(μ).