9709 P53 - Jun 2026 - Q2 - 6 marks
9178
The random variable \(X\) takes the values \(-2,0,1,3\). It is given that \(P(X=x)=k(x+1)^2\), where \(k\) is a constant.
(a) Draw up the probability distribution table for \(X\), giving the probabilities as numerical fractions not involving \(k\). [3]
(b) Find \(\operatorname{Var}(X)\). [3]
