Question: Let Y 1 < Y 2 < < Y n be the order statistics of a random sample of size n from

Let Y₁ < Y₂ < · · · < Y_n be the order statistics of a random sample of size n from a distribution with pdf f(x) = 1, 0 < x < 1, zero elsewhere. Show that the kth order statistic Y_k has a beta pdf with parameters α = k and β = n − k + 1.

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