Let $Z_1, Z_2, ..., Z_{}$ be independent $N(0,1)$ variables, and let \begin{align*} Y = Z^2_1 + Z^2_2 + ... + Z^2_{}. \end{align*} Provide answers to the following to two decimal places.

Part a) Evaluate the moment generating function $M_{Z^2_1}(t)$ of $Z^2_1$ at the point $t =$.


Part b) Evaluate the moment generating function $M_Y(t)$ of $Y$ at the point $t =$.


Part c) Find the mean of $Y$.


Part d) Find the variance of $Y$.