4. The discrete random variable \(X\) has probability function
$$\mathrm { P } ( X = x ) = \begin{array} { l l }
k \left( x ^ { 2 } - 9 \right) , & x = 4,5,6
0 , & \text { otherwise }
\end{array}$$
where \(k\) is a positive constant.
- Show that \(k = \frac { 1 } { 50 }\).
- Find \(\mathrm { E } ( X )\) and \(\operatorname { Var } ( X )\).
- Find \(\operatorname { Var } ( 2 X - 3 )\).