1. ## Expected Value

Find E(X^4) for X ~ N(0,1)

It can't be as simple as u=0 so the answer is 0, so I am at a lost of how to approach this problem.

2. You are finding the fourth moment here..

Look at this link. Lines no 31-36

You can also find the fourth moment by finding the moment generating function of the standard normal distribution. Then find out the fourth derivative of the moment generating function, and equate it at t=0.

remember that the nth derivative of the moment generating function of a distribution gives you the nth moment.