4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{4ecee051-3a6f-4c12-8c53-926e8c3e241f-14_451_976_233_484}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
A continuous random variable \(X\) has the probability density function \(\mathrm { f } ( x )\) shown in Figure 1
$$\mathrm { f } ( x ) = \begin{cases} m x & 0 \leqslant x \leqslant 5
k & 5 < x \leqslant 10.5
0 & \text { otherwise } \end{cases}$$
where \(m\) and \(k\) are constants.
- Show that \(k = \frac { 1 } { 8 }\)
- Find the value of \(m\)
- Find \(\mathrm { E } ( X )\)
- Find the interquartile range of \(X\)