The random variable $$\(X\)$$ has probability generating function $$\(\mathrm{G}_{X}(t)\)$$ given by $$\[ \mathrm{G}_{X}(t)=\frac{1}{5}+p t+q t^{2}, \]$$ where $$\(p\)$$ and $$\(q\)$$ are constants. Find the probability generating function of $$\(Z\)$$. ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ .

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