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).