Poisson Probability Distribution

The Poisson distribution is a type of discrete probability distribution which applies to event occurrences over a specified interval, such as time, volume, distance, or any similar unit.

Consider the data on daily car sales with a mean of three per day. In this case, the Poisson distribution can be used to predict the degree of spread around the mean value.

For instance, it can predict the probability of selling exactly 4 cars on a given day, using the formula for Poisson distribution. This probability value depends only on the mean and not on previous sales history.

Using the same formula, all other probabilities can be calculated and plotted for better visual representation.

The standard deviation for a Poisson distribution is given by the square root of the mean.

Unlike binomial distribution, the Poisson distribution is only affected by the mean and not by sample size or probability. Plus, the random variable in the Poisson distribution has no upper limit.