3 The random variable \(X\) takes the values \(1,2,3,4\). It is given that \(\mathrm { P } ( X = x ) = k x ( x + a )\), where \(k\) and \(a\) are constants.
- Given that \(\mathrm { P } ( X = 4 ) = 3 \mathrm { P } ( X = 2 )\), find the value of \(a\) and the value of \(k\).
- Draw up the probability distribution table for \(X\), giving the probabilities as numerical fractions.
- Given that \(\mathrm { E } ( X ) = 3.2\), find \(\operatorname { Var } ( X )\).