Let X 1 ,X 2 , , X 5 be iid with pdf f(x) e x , 0 x , zero elsewhere Show that (X 1 X 2 ) (X 1 X 2 X 5 ) and its denominator are independent

Question: Let X 1 ,X 2 , . . . , X 5 be iid with pdf f(x) = e x , 0 < x <

Let X₁,X₂, . . . , X₅ be iid with pdf f(x) = e^−x, 0 < x < ∞, zero elsewhere. Show that (X₁ + X₂)/(X₁ + X₂ + · · · + X₅) and its denominator are independent.

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Proof Let x1 x2 be the roots of fx Then X1 X2X1 X2 X5 is the fraction of X1X2X1x 2 x5 Use Sq... View full answer

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