Great video, only let me express to you that you jumped a huge step when introducing the Poisson equation into the one that simplifies to ((n-1)/n)^t. Why did you transform the probability formalization into that equation? A huge step and I think many might lost the track here. It would be nice if you added the explanation in a comment. Thanks.
The data follows a Poisson distribution, so anything would need to be eventually translated into something involving the Poisson formula. It relies on the fact that X1 follows a Poisson (lambda) distribution, sum of x2…xn follows a Poisson ((n-1)lambda) distribution, sum of x1…xn follows a Poisson (n*lambda) distribution
