Table of Contents
Explain in Detail: Notation
There are a few different ways to represent mathematical equations and formulas. The most common way to write an equation is to use the equals sign (=) to indicate that the two sides of the equation are equal. For example, the equation x + y = 5 could be written as:
x + y = 5
Another way to write an equation is to use parentheses to indicate the order of operations. For example, the equation 3×2 + 4x – 5 could be written as:
(3×2) + (4x) – 5
Finally, you can use the letter x to represent any number in an equation. For example, the equation x = 5 could be written as:
x = 5
What is Poisson Distribution?
Poisson distribution is a statistical function that models the probability of a given number of events occurring in a given time period. The function is used to calculate the likelihood of a specific number of events taking place in a given time period, even if the events are not evenly spaced.
The Formula for Poisson Distribution
The Poisson distribution is a probability distribution that is used to model the number of events that occur in a given time interval. The Poisson distribution is most often used to model the number of occurrences of a rare event.
The Poisson distribution is a discrete distribution and has the following formula:
Where:
x is the number of events that have occurred
λ is the average number of events that occur in a given time interval
How to find the Mean and Variance of Poisson Distribution?
The mean and variance of Poisson distribution can be found using the following formulas:
\(mean = \frac{variance}{\lambda}\)
\(variance = \frac{mean^2}{\lambda}\)
Poisson Distribution Properties (Poisson Mean and Variance)
The Poisson distribution has the following properties:
The mean of a Poisson distribution is equal to the variance.
The shape of a Poisson distribution is bell-shaped.
The Poisson distribution is a discrete distribution.
