Let $X_1,X_2,\dots,X_n$ be a random sample from a Standard Norm Dist with MGF $M_X(t)=e^{0.5t^2}$. Let $\overline{X}=\frac{1}{n}(X_1+X_2 +\dots + X_n)$. Determine the MGF of $\overline{X}$.
I managed to get the MGF of $\overline{X}=[M_X(t/n)]^n$ by using the expectation of $e^{t \overline{X}}$. How do I proceed?
Thanks.