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Random Variables - Combining and transforming

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).

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 ...

Solution Summary

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