Question: 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)]

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].

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