Define the moment-generating function $m_{Z}$ of a random variable $Z$. Let $X_{1}, \ldots, X_{n}$ be independent and identically distributed random variables with distribution $\mathcal{N}(0,1)$, and let $Z=X_{1}^{2}+\cdots+X_{n}^{2}$. For $\theta<1 / 2$, show that

$$m_{Z}(\theta)=(1-2 \theta)^{-n / 2} .$$