4 The probability distribution of the random variable \(X\) is given by the formula
$$\mathrm { P } ( X = r ) = k r ( r + 1 ) \quad \text { for } r = 1,2,3,4,5 .$$
- Show that \(k = \frac { 1 } { 70 }\).
- Find \(\mathrm { E } ( X )\) and \(\operatorname { Var } ( X )\).