1. The speed of a molecule in a uniform gas at equilibrium is a random variable whose probability density function is given by

$$f(x) = \begin{cases}

ae^{-bx^2} & x \ge 0 \\

0 & x < 0

\end{cases}$$

where b = m/2kT and k, T, and m denote, respectively, Boltzmann's constant, the absolute temperature, and the mass of the molecule. Evaluate a in terms of b.