$($a$)$ Let $x$ be a random variable with pdf:

$f(x)=\{\begin{array}{cc}\frac{1}{6},& -3x3\\ 0,& \text{o}\text{t}\text{h}\text{e}\text{r}\text{w}\text{i}\text{s}\text{e}& \end{array}$

Find the pdf of $Y=2x^2-3.$ Also find characteristic function of $Y$ and hence its mean

and variance