5 Two random variables \(S\) and \(T\) have probability density functions given by $$\begin{aligned} & f _ { S } ( x ) = \begin{cases} \frac { 3 } { a ^ { 3 } } ( x - a ) ^ { 2 } & 0 \leqslant x \leqslant a
0 & \text { otherwise } \end{cases}
& f _ { T } ( x ) = \begin{cases} c & 0 \leqslant x \leqslant a
0 & \text { otherwise } \end{cases} \end{aligned}$$ where \(a\) and \(c\) are constants.

1. On a single diagram sketch both probability density functions.
2. Calculate the mean of \(S\), in terms of \(a\).
3. Use your diagram to explain which of \(S\) or \(T\) has the bigger variance. (Answers obtained by calculation will score no marks.)