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Expected Minimum of Uniform Random Variables

Medium · Probability & Statistics · Quant Trader interview question · probability, expected-value, order-statistics, uniform-distribution

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: $E\min(X_1, X_2, ..., X_n)$.