A Cool Application of Complex Valued Functions to Probability - Probability-Generating Functions
In this video, I go over probability-generating functions using an example of adding together the result of 2 fair 6 sided dice. I then look at a problem, namely trying to find 2 (possibly differently) distributed biased dice whose sum, when both rolled, will be uniformly distributed. I solve this problem using probability-generating functions which includes using complex numbers!
More information on probability-generating functions: https://en.wikipedia.org/wiki/Probabi...
The slides for this video were made in LaTeX using Beamer (https://ctan.org/pkg/beamer). I used PSTricks (https://ctan.org/pkg/pst-eucl) for the Argand diagrams and a few other packages for other minor details. The presentation was edited and viewed in TeXworks (https://tug.org/texworks/) and recorded with OBS (https://obsproject.com/). I then edited the video with Kdenlive (https://kdenlive.org/en/).