10 The random variable \(X\) has probability density function f given by
$$f ( x ) = \begin{cases} \frac { 1 } { 30 } \left( \frac { 8 } { x ^ { 2 } } + 3 x ^ { 2 } - 14 \right) & 2 \leqslant x \leqslant 4
0 & \text { otherwise } \end{cases}$$
- Find the distribution function of \(X\).
The random variable \(Y\) is defined by \(Y = X ^ { 2 }\). - Find the probability density function of \(Y\).
- Find the value of \(y\) such that \(\mathrm { P } ( Y < y ) = 0.8\).