As a result, for highly occupied states the standard deviation of the particle number of an energy level is very large, slightly larger than the particle number itself: σ σ N ≈ ≈ ⟨ ⟨ N ⟩ ⟩ . This large uncertainty is due to the fact that the probability distribution for the number of bosons in a given energy level is a geometric distribution ; somewhat counterintuitively, the most probable value for N is always 0. (In contrast, classical particles have instead a Poisson distribution in particle number for a given state, with a much smaller uncertainty of σ σ N , c l a s s i c a l = ⟨ ⟨ N ⟩ ⟩ , and with the most-probable N value being near ⟨ ⟨ N ⟩ ⟩ .)