I know Chi-Square distribution. Here the expression is similar to Chi-square distribution with the degree of freedom being 2, except for the square root.
Given: $X_1\ \sim\ N(0,1)\ and\ X_2\ \sim\ N(0,1)$.
$A\ =\ \sqrt{X_1^2\ +\ X_2^2}$
How to find the CDF $F_A(x)$ and PDF $f_A(x)$?
The PDF of $\chi^2$ distribution for $\nu$ degrees of freedom is given by -
$f(\nu^2)\ =\ \frac{1}{2^{\nu / 2}.\Gamma(\nu / 2)}.e^{-\chi^2/2}.(\chi^2)^{\nu/2-1}\ \ ;\ \chi^2\ \geq\ 0$
Can I substitute 2 in place of $\nu$ to get the expression for PDF $f_A(x)$?