7 A continuous random variable \(X\) has probability density function
$$f ( x ) = \left\{ \begin{array} { c c }
k x & 0 \leqslant x < 2
\frac { k ( 4 - x ) ^ { 2 } } { 2 } & 2 \leqslant x \leqslant 4
0 & \text { otherwise }
\end{array} \right.$$
where \(k\) is a constant.
- Show that \(k = \frac { 3 } { 10 }\).
- Find \(\mathrm { E } ( X )\).
- Find the cumulative distribution function of \(X\).
- Find the upper quartile of \(X\), correct to 3 significant figures.
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