5 The random variable \(X\) has probability density function given by
$$f ( x ) = \begin{cases} 4 x ^ { k } & 0 \leqslant x \leqslant 1
0 & \text { otherwise } \end{cases}$$
where \(k\) is a positive constant.
- Show that \(k = 3\).
- Show that the mean of \(X\) is 0.8 and find the variance of \(X\).
- Find the upper quartile of \(X\).
- Find the interquartile range of \(X\).