Let X1,X2X_1, X_2X1,X2 be independent N(0,1)N(0, 1)N(0,1) random variables. What is the distribution of Z=X12+X22Z = X_1^2 + X_2^2Z=X12+X22?
Normal(0,2)\text{Normal}(0, 2)Normal(0,2)
χ2(2)\chi^2(2)χ2(2)
Exponential(0.5)\text{Exponential}(0.5)Exponential(0.5)
Gamma(2,2)\text{Gamma}(2, 2)Gamma(2,2)