Central Limit Theorem is one of the more important concepts in statistics. To put it simply: it explains why that many random processes exhibit normal distribution. Nice visual exploration of this theorem was recently done by 3Blue1Brown. We invite you to watch if you're not yet familiar with the CLT.

Let us assume that you are a college professor. You teach and introductory course, so effectively you have infinitely many students. Any of them can have a chat with you right after the lunch on Friday. Lets say your office hours start around 1 p.m., and end at around 2 p.m.. The problem is that your students are completely unpredictable! But after long years of teaching you have figured out that on average you meet \( 4 \) students each Friday. With \( 95 \% \) confidence what is the maximum number of students that will come to see you?

Five years ago when analyzing rational strategies in a game I have made a mistake. I was so fascinated that for some parameter sets mixed strategy can be used, that I have forgotten, that pure strategy equilibria might still exist and be more attractive than the mixed strategy equilibrium. In this post, I share the updated app.

I like Beta distribution, as it arises from my favorite model - voter model (and Kirman model due to their similarity). There are other, arguably more important, reasons to like it. These are discussed in another excellent statistics video by ritvikmath.

One of the classic agent-based and cellular automata models is so-called forest fire model. It is an excellent example of a modeling problem which could, in theory, be solved using standard mathematical modeling tools (such as, partial differential equations), but it would be extremely hard. On the other hand one could use the aforementioned discrete modeling frameworks. So, lets do that.