CAIE A-Level Further Math A2 4.5.3 Sums of Random Variables Questions

Practise using probability generating functions to combine independent random variables and derive distributions with Further Mathematics AS questions and mark schemes.

Exam points

Use probability generating functions to combine independent random variables.

[Maximum number: 2]

The random variable X has the geometric distribution $\operatorname{Geo}(p)$ .

Find the probability generating function of Z.

$\mathrm{G}_{X}(t)=\frac{\frac{1}{6} t}{1-\frac{5}{6} t} \quad\left[=\frac{t}{6-5 t}\right]$
Implied by correct final answer.

$\mathrm{G}_{z}(t)=\left(\mathrm{G}_{X}(t)\right)^{2}=\left(\frac{t}{6-5 t}\right)^{2}$
Allow $\left(\frac{\frac{1}{6} t}{1-\frac{5}{6} t}\right)^{2}$ .

2

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CAIE A-Level Further Math A2 4.5.3 Sums of Random Variables Questions question 1