Question: Consider the following function

\[f(x)=\left\{ \begin{matrix} k{{(2-x)}^{2}},\begin{matrix} 0\le x\le 2 & {} \\ \end{matrix} \\ 0,\begin{matrix} elsewhere & {} \\ \end{matrix} \\ \end{matrix} \right.\]

a) Find the k in order to make f(x) a valid probability density function.

b) Find P(X>1).

c) Find the expected value of this distribution.

d) Find the median of this distribution.