  Previous critiques of the Drake Equation have highlighted its deterministic
nature, implying that the number of civilizations is the same at all times.
Here, I build upon earlier work and present a stochastic formulation. The birth
of civilizations within the galaxy is modeled as following a uniform rate
(Poisson) stochastic process, with a mean rate of $\lambda_C$. Each then
experiences a constant hazard rate of collapse, which defines an exponential
distribution with rate parameter $\lambda_L$. Thus, the galaxy is viewed as a
frothing landscape of civilization birth and collapse. Under these assumptions,
I show that N in the Drake Equation must follow another Poisson distribution,
with a mean rate $(\lambda_C/\lambda_L)$. This is then used to rigorously
demonstrate why the Copernican Principle does not allow one to infer N, as well
evaluating the algebraic probability of being alone in the galaxy.
