Poisson distribution. Lesson notes

RavshanNovember 27, 2022

Poisson distribution. Lesson notes

While I am writing this lesson notes, Croatia and Canada are playing World Cup 2022 football match in Qatar. Before the start of a game, what can statisticians say about the number of goals in a match based on the historical data? Well, there is a probobability distribution as follows:

Ugarte, M.D.; Militino, A.F.; Arnholt, A.T. (2016). Probability and Statistics with R (2nd ed.).

The current result of the game is 3:1. Total 4 goals have been scored so far. According to the above calculations, there was around 13% probability of 4 goals. (By the time I fineshed, the total number of goals was 5 :) )

In probability theory and statistics, 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 mean rate and independently of the time since the last event.
The Poisson distribution can also be used for the number of events in other specified interval types such as distance, area, or volume.

For instance, a call center receives an average of 180 calls per hour, 24 hours a day. The calls are independent; receiving one does not change the probability of when the next one will arrive. The number of calls received during any minute has a Poisson probability distribution with mean 3: the most likely numbers are 2 and 3 but 1 and 4 are also likely and there is a small probability of it being as low as zero and a very small probability it could be 10.

You may watch the following video to learn how to solve exam problems: