[Exer10-2] Exercise 13 of Book {Devore2017B} P.157
Let $X$ denote checkout time duration with pdf given in Exercise 1 ,
\[
f(x)=\begin{cases}
.5x, & 0\leqslant x\leqslant 2, \\
0, & \mbox{otherwise}.
\end{cases}
\]
- (a) Compute $E(X)$.
- (b) Compute $V(X)$ and $\sigma_X$.
- (c) If the borrower is charged an amount $h(X)=X^2$ when checkout duration is $X$, compute the expected charge $E[h(X)]$.