2 The continuous random variable \(X\) has probability density function defined by
$$f ( x ) = \begin{cases} \frac { 1 } { k } & a \leqslant x \leqslant b
0 & \text { otherwise } \end{cases}$$
- Write down, in terms of \(a\) and \(b\), the value of \(k\).
- Given that \(\mathrm { E } ( X ) = 1\) and \(\operatorname { Var } ( X ) = 3\), find the values of \(a\) and \(b\).
- Four independent values of \(X\) are taken. Find the probability that exactly one of these four values is negative.
[0pt]
[3 marks]