Question

Could you explain the concept of Poisson distribution and how it works, please?

Answer 1

What is the Poisson Distribution?

A Poisson distribution is a device that predicts the likelihood of specific occasions from happening when you know how frequently the occasion has happened. It gives us the likelihood of a given number of occasions occurring in a settled interim of time.

Computing the Poisson Distribution

The Poisson Distribution pmf is: P(x; μ) = (e-μ * μx)/x!

Where:

The symbol "!" is a factorial.

μ (the normal number of events) is at times composed as λ. In some cases called the event rate or rate parameter.

Example

The average number of strom in your city is 2 every year. What is the likelihood that probability 3 strom will hit your city one year from now?

Stage 1: Figure out the segments you have to put into the condition.

μ = 2 (normal number of Strom every year, generally)

x = 3 (the quantity of Strom we think may hit one year from now)

e = 2.71828 (e is Euler's number, a constant)

Stage 2: Plug the qualities from Step 1 into the Poisson distribution formula

P(x; μ) = (e-μ) (μx)/x!

= (2.71828 – 2) (23)/3!

= (0.13534) (8)/6

= 0.180

The likelihood of 3 storms occurring one year from now is 0.180, or 18%

This is how the poisson distribution works

I hope you find this helpful thank you ☺️