2. Let $X \stackrel{d}{=} N\left(\mu, \sigma{2} ight) $ and let $Yra X+b$, where $a neq 0$ and $b \in \mathcal{R} $. (a) Give the moment generating function for $y$. (b) Refer to (a). Apply the Uniqueness Theorem to identify the distribution for $y$. (c) Suppose $\mu=0, \sigma^{2}=25, a=-2$ and $b=2$. Compute $\operatorname(Var}\left(Y^{2} ight) $. (d) Assuming the same specifications in (c), compute $P(-100)$. SP.PC.081