Let $X$ be a normally distributed random variable with mean 0 and variance 1 . Define, and determine, the moment generating function of $X$. Compute $\mathbb{E} X^{r}$ for $r=0,1,2,3,4$.

Let $Y$ be a normally distributed random variable with mean $\mu$ and variance $\sigma^{2}$. Determine the moment generating function of $Y$.