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(Solved): Let X1,...,Xn Be Independent And Identically Distributed Continuous Random Variables And Let X(1),.....

Let X1,...,Xn be independent and identically distributed continuous random variables and let X(1),...,X(n) denote their order statistics. (a) Find P(Xn = X(k)) for k = 1,...,n. Hint: Note that all orderings of X1,...,Xn are equally likely. (b) Show that (Xn,X(n)) does not have a joint pdf.

1. Let X1, ..., Xn be independent and identically distributed continuous random variables and let X(1), ..., X(n) denote thei

1. Let X1, ..., Xn be independent and identically distributed continuous random variables and let X(1), ..., X(n) denote their order statistics. (a) Find P(Xn = X(k)) for k = 1,..., n. Hint: Note that all orderings of X1, ..., Xn are equally likely. (b) Show that (Xn, X(n)) does not have a joint pdf.

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