Let XXX and YYY be independent Exp(1)\text{Exp}(1)Exp(1) variables. What is the PDF of Z=X+YZ = X + YZ=X+Y?
fZ(z)=e−zf_Z(z) = e^{-z}fZ(z)=e−z
fZ(z)=ze−zf_Z(z) = ze^{-z}fZ(z)=ze−z
fZ(z)=z22e−zf_Z(z) = \frac{z^2}{2}e^{-z}fZ(z)=2z2e−z
fZ(z)=e−z−ze−zf_Z(z) = e^{-z} - ze^{-z}fZ(z)=e−z−ze−z