If two random variables have the joint probability density function

\(f(x, y) = \left\{\begin{matrix}Ke^{-(x+y)}, \enspace 0 < x < ∞, \enspace 0 < y < ∞\\ 0, otherwise\end{matrix}\right.\)

Find (i) constant k (ii) Conditional probability density function of X and given Y (iii) Var(3X + 2Y)

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