Moment-generating function of a standard normal variable
= Moment-generating function of a standard normal variable
{title2=$M_Z(t)=e^{t^2/2}$}
Completing the square in the <standard normal density> gives $\mathbb E[e^{tZ}]=e^{t^2/2}$. Differentiating at zero yields $\mathbb E[Z]=0$, $\mathbb E[Z^2]=1$, and $\mathbb E[Z^4]=3$.