Chapter 5, Problem 5.1TE

The speed of a molecule in a uniform gas at equilibrium is a random variable whose probability density function is given by $f\left(x\right)=\{\begin{array}{cc}a{x}^2{e}^{-b{x}^2}& x\ge 0\\ 0& x<0\end{array}$ where $b=\frac{m}{2kT}$ and T, and in denote, respectively, Boltzmann’s constant, the absolute temperature of the gas, and the mass of the molecule. Evaluate a in terms of b.