Question: This problem is related to the equipartition theorem. Consider a system in which the energy of a particle is given by E = Au 2

This problem is related to the equipartition theorem. Consider a system in which the energy of a particle is given by E = Au², where A is a constant and u is any coordinate or momentum that can vary from - ∞ to + ∞.

(a) Write the probability of the particle having u in the range du and calculate the normalization constant C in terms of A.

(b) Calculate the average energy (E) = (Au²) and show that (E) = 1/2 kT.

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