ASSIGNMENT > Math 302, Assignment 8 Solutions
University of British Columbia MATH_V 302 1. Let X ∼ Exp(2), Y ∼ Unif([1, 3]), and assume that X and Y are independent. Calculate P(Y − X ≥ 1 2 ). Solution: The joint density function is f(x, y) = fX(x)fY (y) = ( e−2x if x > 0 and 1 < y < 3, 0 otherwise. Let T be defined by T = {(x, y) : x > 0, 1 < y < 3, x ≤ y − 1/2}, then we have P(Y − X ≥ 1/2) = ZZ T f(x, ...[Show More]
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