CAIE A-Level Further Math A2 4.5.2 Pgf Mean and Variance Questions

Practise using probability generating functions to calculate means and variances for discrete random variables with Further Mathematics AS questions and mark schemes.

Exam points

Use probability generating functions to derive means and variances.

[Maximum number: 2]

Keira has two unbiased coins. She tosses both coins. The number of heads obtained by Keira is denoted by X.

Use the probability generating function of Z to find E(Z).

$\mathrm{G}_{Z}^{\prime}(t)=\frac{1}{144}\left(40+102 t+93 t^{2}+36 t^{3}+5 t^{4}\right)$
Differentiate

$\mathrm{E}(Z)=\mathrm{G}_{Z}^{\prime}(1)=\frac{23}{12}=(=1.92)$
2

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CAIE A-Level Further Math A2 4.5.2 Pgf Mean and Variance Questions question 1