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 per hour runs for hours. Given that exactly 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?
Related concepts
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