9231 P43 - Jun 2021 - Q4 - 8 marks
6800
\(X\) is a discrete random variable which takes the values \(0,2,4, \ldots\). The probability generating function of \(X\) is given by
\(\mathrm{G}_{X}(t)=\frac{1}{3-2 t^{2}} .\)
(a) Find \(\mathrm{E}(X)\) and \(\operatorname{Var}(X)\).
(b) Find \(\mathrm{P}(X=4)\).
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