Binomial count (source code)

= Binomial count
{title2=$K\sim\operatorname{Bin}(n,p)$}

A <binomial count> $K$ records the number of successes in $n$ independent <Bernoulli trials> with common success <probability> $p$. It is the <sum> of the success <indicator variables>, so $K\sim\operatorname{Bin}(n,p)$, with <expected value> $np$ and <variance> $np(1-p)$. Ten independent coin flips give a <binomial count> of heads; ten dependent outcomes generally do not, even if each marginal success <probability> is $p$.