5 The probability distribution of the random variable \(X\) is given by the formula
$$\mathrm { P } ( X = r ) = k + 0.01 r ^ { 2 } \text { for } r = 1,2,3,4,5 \text {. }$$
- Show that \(k = 0.09\). Using this value of \(k\), display the probability distribution of \(X\) in a table.
- Find \(\mathrm { E } ( X )\) and \(\operatorname { Var } ( X )\).