Statistics interview question: What is the difference between a binomial and a Poisson variable?

Statistics is such a complex subject. I am currently watching a video on statistics and the instructor is writing complex formulas on a board for the students to see. When I look at all of the mathematics involved in making accurate statistical work, I am dumbfounded because of all of the complexities in the formulas presented.

It is a good thing then that we are not required to memorise the statistical formulas because my level of knowledge does not extend that far.

One thing that we are required to know, however, is the basic fundamentals of the common statistical distributions. Two distributions that will be discussed in this post are the binomial and Poisson distributions because of their similarity.

Because of the similarities of these two distributions, one question that may be asked at an interview is:-

What is the difference between a binomial and Poisson variable?

In order to answer that question, it is first important to know about the binomial and Poisson distributions.

Binomial variable

A binomial random variable is the number of successes in an experiment consisting of N trials.