3 The continuous random variable $X$ has probability density function f given by

$$f ( x ) = \begin{cases} \frac { 3 } { 16 } ( 2 - \sqrt { x } ) & 0 \leqslant x < 1 \\ \frac { 3 } { 16 \sqrt { x } } & 1 \leqslant x \leqslant 9 \\ 0 & \text { otherwise } \end{cases}$$

(a) Find $\mathrm { E } ( X )$.\\

The random variable $Y$ is such that $Y = \sqrt { X }$.\\
(b) Find the probability density function of $Y$.\\

\hfill \mbox{\textit{CAIE Further Paper 4 2020 Q3}}