7 The random variables \(X\) and \(W\) have probability density functions f and g defined as follows: $$\begin{gathered} \mathrm { f } ( x ) = \begin{cases} p \left( a ^ { 2 } - x ^ { 2 } \right) & 0 \leqslant x \leqslant a
0 & \text { otherwise } \end{cases}
\mathrm { g } ( w ) = \begin{cases} q \left( a ^ { 2 } - w ^ { 2 } \right) & - a \leqslant w \leqslant a
0 & \text { otherwise } \end{cases} \end{gathered}$$ where \(a , p\) and \(q\) are constants.

1. 1. Write down the value of \(\mathrm { P } ( X \geqslant 0 )\).
   2. Write down the value of \(\mathrm { P } ( W \geqslant 0 )\).
   3. Write down an expression for \(q\) in terms of \(p\) only.
2. Given that \(\mathrm { E } ( X ) = 3\), find the value of \(a\).
   If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.