Chapter 15.8, Problem 3P

The probability density function for the $x$ component of the velocity of a molecule of an ideal gas is proportional to $e^{-m{v}^2/(2kT)}$ where $v$ is the $x$ component of the velocity, $m$ is the mass of the molecule, $T$ is the temperature of the gas and $k$ is the Boltzmann constant. By comparing this with ( 8.1), find the mean and standard deviation of v, and write the probability density function $f(v)$.