7 The function \(\mathrm { f } ( x )\) is defined by
$$f ( x ) = \begin{cases} \frac { 1 } { 4 } x \left( 4 - x ^ { 2 } \right) & 0 \leqslant x \leqslant 2
0 & \text { otherwise } \end{cases}$$
- Show that \(\mathrm { f } ( x )\) satisfies the conditions for a probability density function.
- Find the value of \(a\) such that \(\mathrm { P } ( X < a ) = \frac { 15 } { 16 }\).