2. The discrete random variable \(X\) can take only the values 1,2 and 3 . For these values the cumulative distribution function is defined by
$$\mathrm { F } ( x ) = \frac { x ^ { 3 } + k } { 40 } \quad x = 1,2,3$$
- Show that \(k = 13\)
- Find the probability distribution of \(X\).
Given that \(\operatorname { Var } ( X ) = \frac { 259 } { 320 }\)
- find the exact value of \(\operatorname { Var } ( 4 X - 5 )\).