Probability : Poisson Distribution

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On May 22, 1960, in Valdivia, Chile, the largest recorded earthquake with a magnitude of 9.5 occurred.



This week, I decided to refresh my understanding of the math behind the Poisson Distribution (pronounced as "pwah-son").

I first came across it during Lecture 3 of Industrial Statistics, where we were exploring Probability Distributions amidst the pandemic.

Now, you might wonder, "What is a probability distribution?"

In simple terms, it's a way to represent how likely an event is to happen.

So, what makes the Poisson Distribution special? 

It's named after the French mathematician Siméon Denis Poisson, who was fascinated by mortality rates and birth statistics. 

He developed this probability distribution to model events that are both rare and random but occur at a constant average rate —think of earthquakes.


Example

Earthquakes occur on average 3 times per month in Little Garden Island. What is the probability that on a given month there will be no earthquakes using the Poisson Distribution formula?




Where  P(X=k): Probability of having exactly k events.

e: Euler's number, approximately 2.71828.

λ: Average rate of events occurring per unit of time or space.

k: The specific number of events for which you want to find the probability.

k!: Factorial of k, which is the product of all positive integers up to k.


Substituting the values would give you:




Therefore, the probability that on a given month there will be no earthquakes in Little Garden Island is approximately 0.0498 or 4.98%.

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