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Past exam of the mathematics course of the University of Oxford

2023

Prelims

Mathematics III

{c}

Writing $q=1-p$, the <probability generating function> is a <geometric series>:
$$
\boxed{G_N(s)=\mathbb E[s^N]=\sum_{n=0}^\infty p(qs)^n=\frac p{1-qs},\qquad |s|<q^{-1}.}
$$
The displayed restriction ensures <absolute convergence>.

Solution

Past exam of the mathematics course of the University of Oxford / 2023 / Prelims / Mathematics III / 5 / a / ii / Solution

Past exam of the mathematics course of the University of Oxford / 2023 / Prelims / Mathematics III / 5 / a / ii / Solution

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Past exam of the mathematics course of the University of Oxford / 2023 / Prelims / Mathematics III / 5 / a / ii / Solution

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