# Question

According to the Maxwell-Boltzmann law of theoretical physics, the probability density of V, the velocity of a gas molecule, is

Where β depends on its mass and the absolute temperature and k is an appropriate constant. Show that the kinetic energy E = 1/2 mV2, where m the mass of the molecule is a random variable having a gamma distribution.

Where β depends on its mass and the absolute temperature and k is an appropriate constant. Show that the kinetic energy E = 1/2 mV2, where m the mass of the molecule is a random variable having a gamma distribution.

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