In classical thermodynamics the (non-normalized) probability for a single particle amongst a large number of identical particles to have an energy e is given by p(e) = exp(− e kbt ). suppose the energy of the particles in question takes the form e = ax2 , where a is a positive constant, and x is a variable ranging (in whatever units are appropriate) from zero to infinity. show that the average energy for this system is given by hei = kbt 2 . this is known as the equipartition theorem.