Suppose Y1,Y2,··· ,Yn are i.i.d. continuous uniform(0,1) distributed. (a) Prove that the kth-order statistic, Y(k), has Beta distribution with α = k and β = n−k+ 1. (b) What is the distribution of the median of Y1,Y2,··· ,Yn when n is an odd integer? (c) Find the joint density of the middle two of Y(1),Y(2),··· ,Y(n) when n is an even integer

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