13. Suppose X ~ Exp(? = 5) and Y ~ Exp(? = 3). Calculate the following: (a) P(3X + Y ? 3) (b) P(X ? Y) (c) P(3X + Y ? 3)
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- X ~ Exp(λ = 5) with f_X(x) = 5 e^{-5x}, x ≥ 0. - Y ~ Exp(λ = 3) with f_Y(y) = 3 e^{-3y}, y ≥ 0. - Assume X and Y are independent, so f_{X,Y}(x,y) = 15 e^{-5x-3y} for x,y ≥ 0. Show more…
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