Last week I did a brief introduction to the Poisson distribution with my younger son. That project is here:

https://mikesmathpage.wordpress.com/2021/05/09/introducing-some-basic-ideas-about-the-poisson-distribution-to-my-younger-son/

Today I dove in a little more to see if he could see some of the patterns that emerge in the distribution. We started with a quick review and a look at data from a few simulations I ran:

Next we looked at the data from four simulations with an averages of 1, 2, 3, and 4 events expected per year. It was a little hard for him to see the overall pattern, but after a few hints he was able to see what was going on:

To wrap up today, we looked at the pattern from the simulations and tried to write down the pattern that we’d expect to see for an event that happens 5 times per year on average. At the end of this video he was able to write down a formula for the general pattern!