# 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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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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