- The continuous random variable \(X\) has cumulative distribution function given by
$$\mathrm { F } ( x ) = \left\{ \begin{array} { c c }
0 & x < 0
\frac { 1 } { 6 } x ( x + 1 ) & 0 \leqslant x \leqslant 2
1 & x > 2
\end{array} \right.$$
- Find the value of \(a\) such that \(\mathrm { P } ( X > a ) = 0.4\)
Give your answer to 3 significant figures.
- Use calculus to find (i) \(\mathrm { E } ( X )\)
(ii) \(\operatorname { Var } ( X )\).