Bernoulli Processes

A Bernoulli process is a sequence of independent coin flips with success probability \(p\) — the simplest arrival process, and the discrete-time ancestor of the Poisson process.

Time of the \(k^\text{th}\) Arrival

\[Y_k=T_1+\ldots+T_k\]

\[p_{Y_k}(t)=\binom{t-1}{k-1}p^k(1-p)^{t-k},\qquad t=k,k+1,\ldots\]

Draft

This page is a partial draft. The interarrival-time view, and the splitting and merging of Bernoulli processes, remain to be written.