May/June 2026 Paper 53

The random variable $X$ takes the values $-2,0,1,3$. It is given that $\mathrm{P}(X=x)=k(x+1{)}^2$, where $k$ is a constant.

Complete the probability distribution table for $X$, giving each probability as a numerical fraction not involving $k$.

Find the value of $\mathrm{Var}(X)$.