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TL;DR

Central Limit Theorem and Rate of Convergence: 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
olympiadRandom Variables & Distributions

Central Limit Theorem and Rate of Convergence

Asked at: Jane Street, Two Sigma, Citadel

Problem
State the Central Limit Theorem precisely. Then: if X1,…,XnX_1, \ldots, X_n are i.i.d. Bernoulli(1/212\frac{1}{2}), use the CLT to approximate P(Sn≥0.55n)P(S_n \geq 0.55n) for n=100n = 100. How accurate is this approximation (Berry-Esseen bound)?
Related concepts
Central Limit TheoremBerry Esseen

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