This question confused me at the end where it says a normal random variable. A breakdown of the answer would be great
The Question states:
The MGF for the (general) normal distribution is given by Mx(t) = exp(μt + (σ^2)(t^2)/2). Use this to find the mean and variance of a normal random Variable
If you go over your course material again you will find that the n-th moment of a random variable is the n-th derivative of its moment generating function at point t=0.