• Abraham de Moivre (1711): De Mensura Sortis seu; de Probabilitate Eventuum in Ludis a Casu Fortuito Pendentibus

• In general, the Poisson distribution is useful for describing the number of events that occur during a specified time interval.

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\[ P(Outcome = x|\lambda) = \frac{\lambda^xe^{-\lambda}}{x!} \]

\[\lambda = \text{Controls the rate of events}\]

# Probability 2 events per period time with lamda = 3
dpois(2,lambda = 3)
# Probability 2 or fewer events per period time with lamda = 3
ppois(2,3)
# Pseudo-random draw of the number of events when lambda = 3
rpois(1,3)

## [1] 0.2240418
## [1] 0.4231901
## [1] 5

• Suppose we take a window of time and divide it into N sections