1. To learn more about other discrete probability distributions, please refer to the following tutorial: The Poisson distribution is the discrete probability distribution of the number of events occurring in a given time period, given the average number of times the event occurs over that time period. e is the base of logarithm and e = 2.71828 (approx). ${P(X-x)}$ = Probability of x successes. The formula for Poisson Distribution formula is given below: \[\large P\left(X=x\right)=\frac{e^{-\lambda}\:\lambda^{x}}{x! If we let X= The number of events in a given interval. }\] Here, $\lambda$ is the average number x is a Poisson random variable. The arrival of an event is independent of the event before (waiting time between events is memoryless).For example, suppose we own a website which our content delivery network (CDN) tells us goes down on average once per … Example. The Poisson distribution The Poisson distribution is a discrete probability distribution for the counts of events that occur randomly in a given interval of time (or space). Solved Example The number of typing mistakes made by a typist has a Poisson distribution. Poisson Distribution Formula – Example #2. The number of road construction projects that take place at any one time in a certain city follows a Poisson distribution with a mean of 3. A Poisson Process is a model for a series of discrete event where the average time between events is known, but the exact timing of events is random. The vehicles enter to the entrance at an expressway follow a Poisson distribution with mean vehicles per hour of 25. Find the probability that a three-page letter contains no mistakes. You have observed that the number of hits to your web site occur at a rate of 2 a day. The Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant rate and independently of the time since the last event. In this tutorial, you learned about how to use Poisson approximation to binomial distribution for solving numerical examples. When calculating poisson distribution the first thing that we have to keep in mind is the if the random variable is a discrete variable. If however, your variable is a continuous variable e.g it ranges from 1