If f(x 1 , x 2 ) = e x 1 x 2 , 0 < x

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If f(x1, x2) = e−x1−x2 , 0 < x1 < ∞, 0 < x2 < ∞, zero elsewhere, is the joint pdf of the random variables X1 and X2, show that X1 and X2 are independent and that M(t1, t2) = (1 − t1)−1(1 − t2)−1, t2 < 1, t1 < 1. Also show that

Accordingly, find the mean and the variance of Y = X1 + X2.

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Introduction To Mathematical Statistics

ISBN: 9780321794710

7th Edition

Authors: Robert V., Joseph W. McKean, Allen T. Craig

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