Expected Minimum of Uniform Random Variables - Quant Trader Interview Question
Difficulty: Medium
Category: Probability & Statistics
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Topics: probability, expected-value, order-statistics, uniform-distribution
Problem Description
Suppose you are writing a simulation for a trading strategy that relies on multiple independent price feeds. You model the prices from each feed as i.i.d. uniform random variables on the interval $ 0, 1 $. You are interested in the minimum price reported by these feeds.
Let $X_1, X_2, ..., X_n$ be $n$ independent random variables, each uniformly distributed on $ 0, 1 $. Determine the expected value of the minimum of these random variables: $E\min(X_1, X_2, ..., X_n)$.
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