This is a discrete type distribution that is used to model the #frequency of a specific event occurring in a particular period of time or in some specified region. The time #interval could be a second, a minute, a day or a month and a specific #region could be a particular area, volume, length, piece of a paper or any line segment. The Poisson distribution formula is given as P(X=x) = Exp(-mean)*mean^(x) / x! where the random variable X represents the number of times the event occurs. The mean of the Poisson distribution is equal to its variance.
Applications:
The number of phone calls received in a call center per hour.
The number of typological errors per page in an article.
The number of white cells in a blood sample of a dengue patient.
The number of bus arrivals at an intersection per hour or per day.
The number of accidents at an intersection per month.
The number of #coronavirus patients arrive per day in the quarantine of a hospital.
Example 01: During an experiment in a nuclear laboratory, the mean number of radioactive particles passing through a beam in 1 microsecond is 3. Find the probability that 6 particles passing through the beam in a given microsecond? (Ans. 0.0504)
Example 02: The #average number of oil tankers arrive in a refinery is 10 per day. The management of an oil refinery can handle 15 tankers per day. Find the probability that on a given day more than 15 tankers arrive. (Ans. 0.0487)
Example 03: A data entry specialist identified 200 typing mistakes in a report that contain 500 pages. Find the probability of committing exactly three 3 mistakes in a particular page. (Ans. 0.0072)