- A continuous random variable \(X\) has probability density function \(\mathrm { f } ( x )\) where
$$f ( x ) = \left\{ \begin{array} { c c }
k x ^ { n } & 0 \leqslant x \leqslant 1
0 & \text { otherwise }
\end{array} \right.$$
where \(k\) and \(n\) are positive integers.
- Find \(k\) in terms of \(n\).
- Find \(\mathrm { E } ( X )\) in terms of \(n\).
- Find \(\mathrm { E } \left( X ^ { 2 } \right)\) in terms of \(n\).
Given that \(n = 2\)
- find \(\operatorname { Var } ( 3 X )\).