- A discrete random variable \(X\) has the probability function
$$\mathrm { P } ( X = x ) = \begin{cases} k ( 1 - x ) ^ { 2 } & x = - 1,0,1 \text { and } 2
0 & \text { otherwise } \end{cases}$$
- Show that \(k = \frac { 1 } { 6 }\)
- Find \(\mathrm { E } ( X )\)
- Show that \(\mathrm { E } \left( X ^ { 2 } \right) = \frac { 4 } { 3 }\)
- Find \(\operatorname { Var } ( 1 - 3 X )\)