Let X1,X2X_1, X_2X1,X2 be independent 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?
re−r2/2,r≥0r e^{-r^2/2}, r \geq 0re−r2/2,r≥0
e−r2/2,r≥0e^{-r^2/2}, r \geq 0e−r2/2,r≥0
12πe−r2/2\frac{1}{\sqrt{2\pi}} e^{-r^2/2}2π1e−r2/2
re−r,r≥0r e^{-r}, r \geq 0re−r,r≥0