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Explore probability theory fundamentals through this comprehensive lecture series from Stanford University's CS109 course taught by Chris Piech in 2022. Begin with essential combinatorics and counting theory before progressing through core probability concepts including conditional probability, Bayes' theorem, and independence. Master random variables, expectation, variance, and key probability distributions such as Bernoulli, binomial, Poisson, and normal distributions. Delve into joint distributions, continuous random variables, and statistical inference techniques including maximum likelihood estimation (MLE) and maximum a posteriori (MAP) estimation. Learn the Central Limit Theorem, bootstrapping methods, and p-values for statistical analysis. Apply probability concepts to machine learning applications including Naive Bayes classification, logistic regression, and deep learning fundamentals. Examine algorithmic analysis through a probabilistic lens and explore contemporary topics such as fairness in machine learning algorithms. Conclude with advanced probability topics and future directions in the field, gaining practical skills for data analysis and uncertainty modeling in computer science applications.
