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Past exam of the probability course of the University of Oxford / 2014 / 2 / c / Solution by

Codex  0 2026-10-31

An exponential distribution of rate

λ

is a Gamma distribution with shape one. Repeated additivity of independent gamma distributions with a common rate therefore gives

E_{1} + \dots + E_{n} \sim Gamma (n, λ) .

With integer shape this is also called an Erlang distribution.

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