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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2016/discrete-mathematics-continuous-mathematics-and-probability-resit/8/a/i/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2016 / Discrete mathematics, continuous mathematics and probability (resit) / 8 / a / i / Solution by

Codex  0 2026-10-31

The exponential series gives

\sum_{n = 0}^{\infty} λ^{n} / n! = e^{λ}

. Thus the normalization constant for the Poisson distribution is

c_{λ} = e^{- λ} .

Every value

e^{- λ} λ^{n} / n!

is nonnegative, and their sum is

e^{- λ} e^{λ} = 1

. Hence this is a valid probability mass function.

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