Consider two single-particle states, A and B, in a system of fermions, where A = - x and B = + x that

Consider two single-particle states, A and B, in a system of fermions, where εA = µ - x and εB = µ + x that is, level A lies below B same amount that level B lies above µ. Prove that the probability of level B being occupied is the same as the probability of level A being unoccupied. In other words, the Fermi-Dirac distribution is “symmetrical” about the point where ε = µ.