# Poisson Distributioin and Binomial distribution

I have doubts about in which contexts the Poisson distribution and binomial distribution are better suited. I feel that both can be used in similar escenarios. Could you help me resolve this doubt, please ? :)

Hey Nicolás,

Thank you for reaching out!

Let's study the key characteristics of both the binomial and the Poisson

distributions.

Binomial Distribution

1. The binomial distribution models the number of successes in a

fixed number of independent trials.

2. Each trial has only two possible outcomes - success or failure.

3. The probability of success (p) is constant for each trial.

Appropriate use cases for a binomial distribution could be the

following:

1. Estimating the number of heads in 100 coin flips.

2. Estimating the number of defective items in a batch of 20 tested.

Poisson Distribution

1. The Poisson distribution models the number of events occurring in a

fixed interval of time or space, with these events occurring independently

of each other.

2. The rate at which the events occur is constant, and events occur one

at a time.

3. It's particularly useful for rare events.

Appropriate use cases for a Poisson distribution could be the

following:

1. Estimating the number of calls received by a call center in an hour;

2. Estimating the number of meteors observed in the night sky over

a certain period.

In a nutshell, we use a binomial distribution when the number of trials

is fixed, outcomes are binary, and you are interested in the count

of successes. In conrtast, we use a Poisson distribution when we're

focusing on the count of occurrences in a given interval or continuous

space, especially when these occurrences are rare and their exact

number of trials is not well-defined but the rate of occurrence is known.

Hope this helps. Let me know if any part of the theory has remained unclear.

Kind regards,

365 Hristina

Thanks Hristina!

Now is crystal clear.

Nicolás :)