(All Steps) [5 + 5 = 10 pts] Suppose X, Y have joint density f_X,Y(x,y)=25e^-5y, 0≤ x≤ y Find (a) the transform for Z = X + 2Y and (b) use it to find
Question: [5 + 5 = 10 pts]
Suppose X, Y have joint density
\[{{f}_{X,Y}}\left( x,y \right)=25{{e}^{-5y}},\,\,\,0\le x\le y<\infty \]Find (a) the transform for Z = X + 2Y and (b) use it to find \(\operatorname{var}\left( Z \right)\).
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