# Question

In this problem, we formulate an alternative derivation of Equation ( 6.58) which gives the PDF of the order statistic, Ym , which is the th largest of a sequence of random variables, X1 ,X2, XN. Start by writing Ym (y) dy = Pr(y < Ym < y + dy). Then note that Pr(y < Ym < y + dy) = Pr ({m–1 of the Xs are less than y}∩ {1 X is between y and y + dy} ∩ {n –m of the Xs are greater than y}).

Find the probability of the above event and by doing so, prove that the PDF of Ym is as given by Equation (6.58).

Find the probability of the above event and by doing so, prove that the PDF of Ym is as given by Equation (6.58).

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