1. Why did Poisson invent Poisson Distribution?

To predict the # of events occurring in the future!

More formally, to predict the probability of a given number of events occurring in a fixed interval of time.

If you’ve ever sold something, this “event” can be defined, for example, as a customer purchasing something from you (the moment of truth, not just browsing). It can be how many visitors you get on your website a day, how many clicks your ads get for the next month, how many phone calls you get during your shift, or even how many people will die from a fatal disease next year, etc.

Below is an example of how I’d use Poisson in real life.

Every week, on average, 17 people clap for my blog post. I’d like to predict the # of ppl who would clap next week because I get paid weekly by those numbers. What is the probability that exactly 20 people (or 10, 30, 50, etc.) will clap for the blog post next week?

2. For now, let’s assume we don’t know anything about the Poisson Distribution. Then how do we solve this problem?

One way to solve this would be to start with the number of reads. Each person who reads the blog has some probability that they will really like it and clap.

This is a classic job for the binomial distribution, since we are calculating the probability of the number of successful events (claps).

A binomial random variable is the number of successes x in n repeated trials. And we assume the probability of success p is constant over each trial.

However, here we are given only one piece of information — 17 ppl/week, which is a “rate” (the average # of successes per week, or the expected value of x). We don’t know anything about the clapping probability p, nor the number of blog visitors n.

Therefore, we need a little more information to tackle this problem. What more do we need to frame this probability as a binomial problem? We need two things: the probability of success (claps) p & the number of trials (visitors) n.

Let’s get them from the past data.