Refer to Sec. 6.2 and show that, if the occupation number nε of an energy level ε is restricted to the values 0,1,…,l, then the mean occupation number of that level is given by
⟨nε⟩=z−1eβε−11−(z−1eβε)l+1−1l+1.
Check that while l=1 leads to ⟨nε⟩F.D., l→∞ leads to ⟨nε⟩B.E..