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TL;DR

KL Divergence and Optimal Hypothesis Testing: A canonical quantitative trading interview question at olympiad difficulty. Commonly asked at Jane Street, Two Sigma, Citadel.

By Valenke Exam Prep Team·Last updated 2026-06-01
olympiadInformation & Entropy

KL Divergence and Optimal Hypothesis Testing

Asked at: Jane Street, Two Sigma, Citadel

Problem
You observe nn independent samples from either distribution PP (fair coin, p=1/2p = 12\frac{1}{2}) or QQ (biased coin, q=0.6q = 0.6). Using the KL divergence DKL(PQ)D_{KL}(P \| Q), determine the rate at which the probability of misidentification decreases with nn.

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