4 The continuous random variable \(X\) has probability density function given by
$$f ( x ) = \begin{cases} \frac { 3 } { 2 } \sqrt { x } & 0 < x \leqslant 1
0 & \text { otherwise } \end{cases}$$
The random variable \(Y\) is given by \(Y = \frac { 1 } { \sqrt { X } }\).
- Find the (cumulative) distribution function of \(Y\), and hence show that its probability density function is given by
$$\mathrm { g } ( y ) = \frac { 3 } { y ^ { 4 } }$$
for a set of values of \(y\) to be stated.
- Find the value of \(\mathrm { E } \left( Y ^ { 2 } \right)\).