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TL;DR

MLE for Normal Variance and Bias Correction: A canonical quantitative trading interview question at foundation difficulty. Commonly asked at Two Sigma, Citadel, DE Shaw.

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

MLE for Normal Variance and Bias Correction

Asked at: Two Sigma, Citadel, DE Shaw

Problem
Given i.i.d. samples X1,…,Xn∼N(μ,σ2)X_1, \ldots, X_n \sim N(\mu, \sigma^2) with both parameters unknown, derive the maximum likelihood estimator for σ2\sigma^2. Show that it is biased and find the bias correction factor.
Related concepts
Maximum LikelihoodBias Variance

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