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TL;DR

MLE for Uniform Distribution: A canonical quantitative trading interview question at intermediate difficulty. Commonly asked at Two Sigma, Citadel, DE Shaw, Jump Trading.

By Valenke Exam Prep Team·Last updated 2026-06-01
intermediateStatistical Inference & Estimation

MLE for Uniform Distribution

Asked at: Two Sigma, Citadel, DE Shaw, Jump Trading

Problem
You observe nn i.i.d. samples X1,…,XnX_1, \ldots, X_n from Uniform(0,θ)\text{Uniform}(0, \theta) where θ>0\theta > 0 is unknown. Find the maximum likelihood estimator θ^MLE\hat{\theta}_{\text{MLE}}. Is it unbiased? If not, correct it.
Related concepts
Maximum LikelihoodOrder Statistics

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