The probability generating function, \(\mathrm{G}_{Y}(t)\), of the random variable \(Y\) is given by
\(\mathrm{G}_{Y}(t)=0.04+0.2 t+0.37 t^{2}+0.3 t^{3}+0.09 t^{4}\)
(a) Find \(\operatorname{Var}(Y)\).

The random variable \(Y\) is the sum of two independent observations of the random variable \(X\).
(b) Find the probability generating function of \(X\), giving your answer as a polynomial in \(t\).