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 Incoming links: Geometric minimum law

Past exam of the year 1 of the computer science course of the University of Oxford / 2017 / Discrete mathematics, continuous mathematics and probability / 7 / a / iv / Solution 2026-10-31

By independence, for

k \geq 0

,

P (W > k) = P (X_{1} > k, X_{2} > k) = (1 - p)^{2 k} .

This is the geometric minimum law, giving

W \sim Geom (1 - (1 - p)^{2}) = Geom (2 p - p^{2}) .

The support remains the positive integers; this parameter is a success probability, not a mean.

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