7 Two continuous random variables \(S\) and \(T\) have probability density functions \(\mathrm { f } _ { S }\) and \(\mathrm { f } _ { T }\) given respectively by $$\begin{aligned} & f _ { S } ( x ) = \begin{cases} \frac { a } { x ^ { 2 } } & 1 \leqslant x \leqslant 3
0 & \text { otherwise } \end{cases}
& f _ { T } ( x ) = \begin{cases} b & 1 \leqslant x \leqslant 3
0 & \text { otherwise } \end{cases} \end{aligned}$$ where \(a\) and \(b\) are constants.

1. Sketch on the same axes the graphs of \(y = \mathrm { f } _ { S } ( x )\) and \(y = \mathrm { f } _ { T } ( x )\).
2. Find the value of \(a\).
3. Find \(\mathrm { E } ( S )\).
4. A student gave the following description of the distribution of \(T\) : "The probability that \(T\) occurs is constant". Give an improved description, in everyday terms.