Let XXX and YYY be independent N(0,1)N(0, 1)N(0,1) variables. What is the PDF of Z=X2+Y2Z = X^2 + Y^2Z=X2+Y2?
fZ(z)=12e−z/2f_Z(z) = \frac{1}{2}e^{-z/2}fZ(z)=21e−z/2 for z>0z > 0z>0
fZ(z)=e−zf_Z(z) = e^{-z}fZ(z)=e−z for z>0z > 0z>0
fZ(z)=ze−z2/2f_Z(z) = z e^{-z^2/2}fZ(z)=ze−z2/2 for z>0z > 0z>0
fZ(z)=12πe−z/2f_Z(z) = \frac{1}{\sqrt{2\pi}} e^{-z/2}fZ(z)=2π1e−z/2 for z>0z > 0z>0