Day 171 · Jun 19

Birthday of Siméon Denis Poisson (1781)

Poisson studied under Lagrange and Laplace and made fundamental contributions to probability and mathematical physics. The Poisson distribution models the number of rare events in a fixed time: if the average rate is λ, the probability of exactly k events is e^(−λ)λᵏ/k!. It models phone calls arriving at a switchboard, radioactive decays per minute, and emails per hour. The distribution was first applied to the number of Prussian soldiers kicked to death by horses per year — a grim but precise use of mathematics to find pattern in tragedy.

If a server receives on average 3 requests per second, what is the probability of receiving exactly 5 requests in a given second? Use P(k) = e^(−3) × 3⁵/5!

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