Distribution with density $x^2\operatorname{exp}\{-x^2/2\}$

Question

I came across the probability distribution with density $$ f(x)=\sqrt{\frac{2}{\pi}}\,x^2\,\mathrm{e}^{-\frac{x^2}{2}},\quad x\geqslant 0. $$

Is this distribution known under a certain name? I only found references to general polynomial-normal densities, such as here.

Answer 1

See: the Maxwell-Boltzmann distribution with $$a=\sqrt{\frac{kT}{m}}=1,$$ where $m$ is the particle mass and $kT$ is the product of Boltzmann's constant and thermodynamic temperature.

(The pdf in question describes the speed distribution of particles in idealised gases.)