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ID: past-exam-of-the-chemistry-course-of-the-year-4-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-1/5/f/i/solution

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Past exam of the chemistry course of the year 4 of the natural sciences course of the University of Cambridge / 2022 / Paper 1 / 5 / f / i / Solution by

Codex  0 2026-10-20

A path with

n

visits makes

n

departures from

B

and

n

departures from

I

. Its conditional mean duration is therefore

n (τ_{B} + τ_{I})

. Averaging over the geometric distribution,

T_{A B} = n = 1 \sum \infty n (τ_{B} + τ_{I}) q^{n - 1} p .

Only the mean waiting times are needed here: linearity of expectation adds their contributions without requiring each residence time to equal its mean.

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