Poisson Distribution is a probability distribution that is used to model the number of times an event occurs in a given time period. It is often used to calculate the likelihood of rare events, such as the number of customers arriving at a store in a given hour or the number of accidents on a highway in a day.
There are three main assumptions for using Poisson Distribution: 1) The probability of an event occurring in a given time interval is constant. 2) The events are independent of each other. 3) The events cannot occur more than once within a given time interval.
The mean and variance for Poisson Distribution are equal and can be calculated using the formula: λ = np, where λ (lambda) is the mean and p is the probability of an event occurring. The standard deviation can be calculated as the square root of the mean (or variance).
Poisson Distribution is used for discrete data, while Normal Distribution is used for continuous data. Poisson Distribution is used to model rare events, while Normal Distribution is used to model a wide range of data. Additionally, the shape of the curves for the two distributions is different, with Poisson Distribution being skewed to the right and Normal Distribution being symmetric.
Poisson Distribution is commonly used in various fields, such as finance, insurance, and telecommunications, to model events such as customer arrivals, insurance claims, and network failures. It is also used in biology to model the number of mutations in a DNA sequence and in sports to model the number of goals scored in a game.