Geometric pair-number distribution ($P(n)=(1-r)r^n$)

The pair count of a two-mode squeezed vacuum has $P(n)=(1-r)r^n$, where $r=|q{|}^2<1$. Its mean is $r/(1-r)$ and its variance is $r/(1-r{)}^2$. Equal mode occupations follow from pair creation, not from independent particle and antiparticle draws.