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

$$F ( x ) = \begin{cases} 0 & x < 0 \\ \frac { 1 } { 60 } \left( 16 x - x ^ { 2 } \right) & 0 \leqslant x \leqslant 6 \\ 1 & x > 6 \end{cases}$$

(a) Find the interquartile range of $X$.\\

(b) Find $\mathrm { E } \left( X ^ { 3 } \right)$.\\

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

If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.\\

\hfill \mbox{\textit{CAIE Further Paper 4 2020 Q6}}