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 ? :)
Thank you for reaching out!
Let's study the key characteristics of both the binomial and the Poisson
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
1. Estimating the number of heads in 100 coin flips.
2. Estimating the number of defective items in a batch of 20 tested.
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
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.