Problem bank

Problem 95 of 333MediumStatisticsP095

Expected gap between order statistics

  1. X1,…,Xn∼Uniform(0,1)X_1, \ldots, X_n \sim \text{Uniform}(0, 1). What is the expected gap between adjacent order statistics, E[X(k+1)−X(k)]E[X_{(k+1)} - X_{(k)}]?