3 A continuous random variable \(X\) has probability density function
$$f ( x ) = \left\{ \begin{array} { c l }
\frac { 3 } { 2 a ^ { 3 } } x ^ { 2 } & - a \leqslant x \leqslant a
0 & \text { otherwise }
\end{array} \right.$$
where \(a\) is a constant.
- It is given that \(\mathrm { P } ( - 3 \leqslant X \leqslant 3 ) = 0.125\). Find the value of \(a\) in this case.
- It is given instead that \(\operatorname { Var } ( X ) = 1.35\). Find the value of \(a\) in this case.
- Explain the relationship between \(x\) and \(X\) in this question.