6 Darts are thrown at random at a circular board. The darts hit the board at distances \(X\) centimetres from the centre, where \(X\) is a random variable with probability density function given by
$$f ( x ) = \begin{cases} \frac { 2 } { a ^ { 2 } } x & 0 \leqslant x \leqslant a
0 & \text { otherwise } \end{cases}$$
where \(a\) is a positive constant.
- Verify that f is a probability density function whatever the value of \(a\).
It is now given that \(\mathrm { E } ( X ) = 8\).
- Find the value of \(a\).
- Find the probability that a dart lands more than 6 cm from the centre of the board.