3 The continuous random variable $X$ has cumulative distribution function F given by

$$F ( x ) = \begin{cases} 0 & x < 0 \\ \frac { 1 } { 81 } x ^ { 2 } & 0 \leqslant x \leqslant 9 \\ 1 & x > 9 \end{cases}$$

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

(b) Find $\operatorname { Var } ( \sqrt { X } )$.\\

(c) The random variable $Y$ is given by $Y ^ { 3 } = X$. Find the probability density function of $Y$.\\

\hfill \mbox{\textit{CAIE Further Paper 4 2021 Q3}}