Tag Archives: poisson distribution

Conditioning and a sum of Poisson random variables

Previously we talked about the Poisson distribution. The Poisson distribution with mean $\mu \gt 0$ is a distribution on the natural numbers whose density function is $$f(n) = \frac{e^{-\mu}\mu^n}{n!}$$ We have already seen that the Poisson distribution essentially arises from the binomial distribution as a sort of "limiting case". In fact, the Poisson distribution is […]

Where does the Poisson distribution come from?

The Poisson distribution is a discrete probability distribution on the natural numbers $0,1,2,\dots$. Its density function depends on one parameter $\mu$ and is given by $$d(n) = \frac{e^{-\mu}\mu^n}{n!}$$ Not surprisingly, the parameter $\mu$ is the mean, which follows from the exponential series $$e^x = \sum_{n=0}^\infty \frac{x^n}{n!}$$ Here is what the density function looks like when […]