Statistics Interview Question: What is the difference between a binomial and a Poisson variable?

The binomial and Poisson distributions are two common discrete distributions. The binomial and Poisson distributions may seem similar, but they do have differences in their makeup and how they are used in statistics and determining probabilities.

Binomial distribution

The binomial distribution is one of the most popular distributions in statistics. In order to understand the binomial distribution, it is first necessary to understand binomial experiments.

The binomial experiment

A binomial experiment has the following properties:-

1. The experiment consists of n repeated trials.
2. Each trial has only two possible outcomes.
3. The probability of success, p, is the same for each trial.
4. Each trial is independent.

Perhaps the most common example of the binomial experiment where a coin is tossed ten times because:-

1. The experiment consists of ten repeated trials.
2. Each trial has only two possible outcomes, being heads or tails.
3. The probability of success is the same for each trial, being 0.5 in this instance.