# Probability

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

given by f(x) = (ax2e−bx2 x>_0 { 0 x < 0

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.

(Additionaly, its ax(to the 2nd)e (to the -bx(to the 2nd) and then x is greater than or equal to 0)

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#### Solution Summary

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

given by f(x) = (ax2e−bx2 x>_0 { 0 x < 0

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.

(Additionaly, its ax(to the 2nd)e (to the -bx(to the 2nd) and then x is greater than or equal to 0)