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    Random Variables - Combining and transforming

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    Let X and Y have the joint pdf f x,y(x,y) = 4e^-x-4y for x>0 and y>0. Define Z=X+Y. Find fz(z).

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    https://brainmass.com/statistics/random-variables/random-variables-combining-and-transforming-9189

    Solution Preview

    Z = X +Y
    Let,
    w = y
    => y = w; x = Z - w
    y>0 => w >0
    x > 0 => z > w
    Jacobian J(x,y) :
    j11 = dZ/dx = 1; j12 = dZ/dy ...

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