The random variable $$\(X\)$$ has probability generating function $$\(\mathrm{G}_{X}(t)\)$$ given by $$\[ \mathrm{G}_{X}(t)=\frac{1}{5}+p t+q t^{2}, \]$$ where $$\(p\)$$ and $$\(q\)$$ are constants. Find $$\(\mathrm{P}(Z> 2)\)$$. ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ .
Exam No:9231_w24_qp_42 Year:2024 Question No:2(c)
Answer:

Knowledge points:
4.5.2 use formulae for the mean and variance of a discrete random variable in terms of its PGF, and use these formulae to calculate the mean and variance of a given probability distribution
Solution:
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