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ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2010/paper-1/12/c/solution

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Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2010 / Paper 1 / 12 / c / Solution by

Codex  0 2026-10-18

The meeting position

N

is the sum of

F

independent Bernoulli random variables, each of mean

p

pq

. Linearity of expectation and variance additivity for independent random variables give

μ = Fp, σ^{2} = Fpq .

These are the mean and variance of the unwrapped integer label specified in the question, rather than circular angular statistics.

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