Consider N = Zi=o Ni >> 1 ideal bosons with mass m are confined within a volume of V and ni is the population in the i-th eigenstate. Given a grand canonical ensemble with chemical potential u and temperature T, the probability to find a = 0,1,2 ... bosons in the state is pa o e-B(aEi-an) where B = 1 KBT A. Show that the mean population Ni = in the state is exactly given by the 1 Bose-Einstein distribution Ni = e B(Ei-M)-1