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(Solved): 2. Let X1, ..., Xn Be Independent Exponential Random Variables With Parameter X, And Let X (1), ...,...

2. Let X1, ..., Xn be independent exponential random variables with parameter X, and let X (1), ..., X (n) be their order sta

2. Let X1, ..., Xn be independent exponential random variables with parameter X, and let X (1), ..., X (n) be their order statistics. Show that Y = nX(1), Y, = (n +1-r)(X(r) - X(n-1)), r= 2, ..., are also independent and have the same joint distribution as X1,..., X. Hint: You may use the fact that the determinant of a lower triangular matrix (a square matrix whose entries above the main diagonal are all zero) is the product of the diagonal entries.

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