Compute probability second largest is below 2/3
Company: Capital One
Role: Data Scientist
Category: Statistics & Math
Difficulty: medium
Interview Round: Technical Screen
Let U1, U2, U3 be i.i.d. Uniform(0,1). Compute P(U(2) < 2/3), where U(2) is the second largest (i.e., the second order statistic). Derive it two ways: (i) using the CDF of the k-th order statistic, and (ii) by interpreting it as “at least two samples fall below 2/3” via a Binomial model.
Quick Answer: This question evaluates understanding of order statistics, uniform probability distributions, and probabilistic reasoning, specifically the ability to relate order-statistic events to counting/binomial interpretations and compute corresponding probabilities.
