- #1
joserse46
- 4
- 0
f(x,y) = (1/x) for 0≤y≤x≤1
A new rv Z=X+Y where X,Y not independent find the pdf of z
My approach
F(z) = P(Z≤z) = ∫∫fXY(x,y) dx dy x= -∞ to ∞ y= 0 to z-y
f(z) = d/dz(F(z)) = ∫fXY(z-y,y) dy y= -∞ to ∞ (using Leibnitz)
where i am stuck is this doesn't converge
A new rv Z=X+Y where X,Y not independent find the pdf of z
My approach
F(z) = P(Z≤z) = ∫∫fXY(x,y) dx dy x= -∞ to ∞ y= 0 to z-y
f(z) = d/dz(F(z)) = ∫fXY(z-y,y) dy y= -∞ to ∞ (using Leibnitz)
where i am stuck is this doesn't converge
