$X$ is the random variable input, and is uniform on $[−20, 20]$. This is input to an “amplitude limiter”, whose output, a new random variable $Y$, relates to the input $X$ as follows: $ Y= \begin{cases} -5, \quad x\leq -5,\\ x,\quad x\in [-5,5],\\ 5,\quad x\geq 5 \end{cases} $
1) Plot the PDF of $X$ and $Y$.
2) Find $E[X]$ and $E[Y]$.
3) Find $E[X^2]$ and $E[Y^2]$.
4) Find the distribution of $Y$ conditioned on $B=\{|x|<1\}$.
This is what I have tried to solve so far:
1) The PDF of $X$ $ =\begin{cases} \tfrac{1}{40},\quad -20