The random variable \(X\) has a continuous uniform distribution over the interval [5,a], where \(a\) is a constant.
Given that \(\operatorname { Var } ( X ) = \frac { 27 } { 4 }\)
show that \(a = 14\)
The continuous random variable \(Y\) has probability density function
$$f ( y ) = \left\{ \begin{array} { c c }
\frac { 1 } { 20 } ( 2 y - 3 ) & 2 \leqslant y \leqslant 6
0 & \text { otherwise }
\end{array} \right.$$
The random variable \(T = 3 \left( X ^ { 2 } + X \right) + 2 Y\)
Show that \(\mathrm { E } ( T ) = \frac { 9857 } { 30 }\)