4 A random variable $X$ has probability density function given by

$$\mathrm { f } ( x ) = \begin{cases} k ( 3 - x ) & 1 \leqslant x \leqslant 2 \\ 0 & \text { otherwise } \end{cases}$$

where $k$ is a constant.\\
(i) Show that $k = \frac { 2 } { 3 }$.\\
(ii) Find the median of $X$.

\hfill \mbox{\textit{CAIE S2 2015 Q4}}