- The continuous random variable \(X\) has probability density function given by
$$f ( x ) = \left\{ \begin{array} { c c }
k ( x + 1 ) ^ { 2 } & - 1 \leqslant x \leqslant 1
k ( 6 - 2 x ) & 1 < x \leqslant 3
0 & \text { otherwise }
\end{array} \right.$$
where \(k\) is a positive constant.
- Sketch the graph of \(\mathrm { f } ( x )\).
- Show that the value of \(k\) is \(\frac { 3 } { 20 }\)
- Define fully the cumulative distribution function \(\mathrm { F } ( x )\).
- Find the median of \(X\), giving your answer to 3 significant figures.