Chapter 5, Problem 5.11TE

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

a. Show that $E\left[g’\left(Z\right)\right]=E\left[Zg\left(Z\right)\right];$

b. Show that $E\left[Z^{n+1}\right]=nE\left[Z^{n-1}\right]$.

c. Find $E\left[Z^4\right]$.