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Let (X,Y ) be a vector of two continuous random variables, with the following joint probability density function (joint PDF), f(x,y) = { e?3y, if

Let (X,Y ) be a vector of two continuous random variables, with the following joint probability density function (joint PDF), f(x,y) = { e?3y, if 0 ?x,y

1. Find the joint PDF of the variables S = X + Y and T = X. 2. Find the marginal PDF of S.

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4. (10 pts) Let (X, Y ) be a vector of two continuous random variables, with the following joint probability density function (joint PDF), f(x, y) = e 3y if 0 ; 0, otherwise. 1. Find the joint PDF of the variables S = X + Y and T = X. 2. Find the marginal PDF of S

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