Let XXX and YYY be i.i.d. N(0,1)N(0, 1)N(0,1). What is the distribution of Z=X2+Y2Z = X^2 + Y^2Z=X2+Y2?
χ2(1)\chi^2(1)χ2(1)
χ2(2)\chi^2(2)χ2(2)
Exponential(1/2)\text{Exponential}(1/2)Exponential(1/2)
Gamma(2,2)\text{Gamma}(2, 2)Gamma(2,2)