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

f(v)=kv^2*e^(- βv^2), for v>0; =0, elsewhere.

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