5. The discrete random variable \(X\) has the probability function
$$\mathrm { P } ( X = x ) = \begin{cases} k x & x = 2,4,6
k ( x - 2 ) & x = 8
0 & \text { otherwise } \end{cases}$$
where \(k\) is a constant.
- Show that \(k = \frac { 1 } { 18 }\)
- Find the exact value of \(\mathrm { F } ( 5 )\).
- Find the exact value of \(\mathrm { E } ( X )\).
- Find the exact value of \(\mathrm { E } \left( X ^ { 2 } \right)\).
- Calculate \(\operatorname { Var } ( 3 - 4 X )\) giving your answer to 3 significant figures.