4. A continuous random variable \(X\) has the cumulative distribution function
$$\mathrm { F } ( x ) = \left\{ \begin{array} { l }
0
\frac { 1 } { 84 } \left( x ^ { 2 } - 16 \right)
1
\end{array} \right.$$
$$\begin{aligned}
& x < 4 ,
& 4 \leq x \leq 10 ,
& x > 10 .
\end{aligned}$$
- Find the median value of \(X\).
- Find the interquartile range for \(X\).
- Find the probability density function \(\mathrm { f } ( x )\) of \(X\).
- Sketch the graph of \(\mathrm { f } ( x )\) and hence write down the mode of \(X\), explaining how you obtain your answer from the graph.
\section*{STATISTICS 2 (A) TEST PAPER 1 Page 2}