If X1,X2X_1, X_2X1,X2 are i.i.d. N(0,1)N(0, 1)N(0,1), what is the PDF of R=X12+X22R = \sqrt{X_1^2 + X_2^2}R=X12+X22?
f(r)=re−r2/2,r≥0f(r) = r e^{-r^2/2}, r \ge 0f(r)=re−r2/2,r≥0
f(r)=e−rf(r) = e^{-r}f(r)=e−r
f(r)=r22e−rf(r) = \frac{r^2}{2} e^{-r}f(r)=2r2e−r
f(r)=12πe−r2/2f(r) = \frac{1}{\sqrt{2\pi}} e^{-r^2/2}f(r)=2π1e−r2/2