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TL;DR

Poisson Conditioning: Uniform Order Statistics: A canonical quantitative trading interview question at olympiad difficulty. Commonly asked at Jane Street, Two Sigma, DE Shaw, Citadel, HRT.

By Valenke Exam Prep Team·Last updated 2026-06-01
olympiadRandom Variables & Distributions

Poisson Conditioning: Uniform Order Statistics

Asked at: Jane Street, Two Sigma, DE Shaw, Citadel, HRT

Problem
A Poisson process with rate λ=5\lambda = 5 per hour runs for T=2T = 2 hours. Given that exactly n=4n = 4 events occurred: (a) What is the joint distribution of the 4 arrival times? (b) What is the expected time of the 2nd arrival? (c) What is the probability that all 4 arrivals happened in the first hour?

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