4. A continuous random variable \(X\) has probability density function
$$\begin{array} { l l }
\mathrm { f } ( x ) = 0 & x < 1 ,
\mathrm { f } ( x ) = k x & 1 \leq x \leq 4 ,
\mathrm { f } ( x ) = 0 & x > 4 .
\end{array}$$
- Sketch a graph of \(\mathrm { f } ( x )\), and hence find the value of \(k\).
- Calculate the mean and the variance of \(X\).
\section*{STATISTICS 2 (A)TEST PAPER 4 Page 2}