# Question: Let Z be a standard normal random variable Z and

Let Z be a standard normal random variable Z, and let g be a differentiable function with derivative g′.

(a) Show that E[g′(Z)] = E[Zg(Z)]

(b) Show that E[Zn+1] = nE[Zn−1]

(c) Find E[Z4].

(a) Show that E[g′(Z)] = E[Zg(Z)]

(b) Show that E[Zn+1] = nE[Zn−1]

(c) Find E[Z4].

## Relevant Questions

Use the identity of Theoretical Exercise 5 to derive E[X2] when X is an exponential random variable with parameter λ. Theoretical Exercise 5 Use the result that, for a nonnegative random variable Y, to show that, for a ...Verify that Var(X) = α / λ2 when X is a gamma random variable with parameters α and λ. Prove Corollary 2.1. Two points are selected randomly on a line of length L so as to be on opposite sides of the midpoint of the line. [In other words, the two points X and Y are independent random variables such that X is uniformly distributed ...If X1 and X2 are independent exponential random variables with respective parameters λ1 and λ2, find the distribution of Z = X1/X2. Also compute P{X1 < X2}.Post your question