You may want to watch my previous video on the generating functions: https://www.youtube.com/watch?v=YB7qnuo-GRY
If you want to know more about the usage of generating functions in network science, check out this paper: https://journals.aps.org/pre/pdf/10.1103/PhysRevE.64.026118 or Mark Newman's "Networks" book: https://www.amazon.com/Networks-Mark-Newman/dp/0198805098
Chapters:
0:00 Poisson distribution
0:38 Probability generating function review
2:20 Probability generating function for Bernoulli process and binomial distribution
6:08 What happens to PGF of binomial distribution when N goes to infinity?
9:30 Connection between binomial and Poisson -- Intuition
9:58 Application to network science (ER random graph model)
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Website: https://yongyeol.com
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