8 A continuous random variable \(X\) has probability density function given by the following function, where \(a\) is a constant.
\(\mathrm { f } ( x ) = \left\{ \begin{array} { l l } \frac { 2 x } { a ^ { 2 } } & 0 \leqslant x \leqslant a ,
0 & \text { otherwise. } \end{array} \right\}\)
The expected value of \(X\) is 4 .

1. Show that \(a = 6\). Five independent observations of \(X\) are obtained, and the largest of them is denoted by \(M\).
2. Find the cumulative distribution function of \(M\). \section*{OCR} Oxford Cambridge and RSA