These videos are great for getting to understand the logic behind the notation. Thanks. If you still manage this account you might consider creating a playlist(s) for these videos so that viewers are taken straight to the next slide. More views for you maybe, and we don't have to get random stuff in our "up next" autoplay video.
How does the geometric proof account for the f(*) factor? This is not probability. The RVs are continuous so f(*) needs to be obtained by taking derivatives. How do you know the derivative works out with the fixed observation x_(k)?