3 The score, \(X\), obtained on a given throw of a biased, four-faced die is given by the probability distribution
$$\mathrm { P } ( X = r ) = k r ( 8 - r ) \text { for } r = 1,2,3,4 .$$
Show that \(k = \frac { 1 } { 50 }\).
Calculate \(\mathrm { E } ( X )\) and \(\operatorname { Var } ( X )\).