= Grand-canonical single-level occupation variance
{title2=$\operatorname{Var}n=\bar n(1\mp\bar n)$}
For one <independent> <fermion> level, occupations 0 and 1 form a <Bernoulli distribution> and give $\operatorname{Var}n=\bar n(1-\bar n)$. For one ideal <boson> level in contact with a reservoir, its <geometric distribution> gives $\operatorname{Var}n=\bar n(1+\bar n)$. Both approach <variance> equal to mean at small occupation. Pauli exclusion suppresses fluctuations of nearly full <fermion> states, whereas large <boson> occupation gives <variance> of order mean squared. Fixed-total-number constraints change condensate fluctuation statements.
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