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Probabilistic Systems Analysis and Applied Probability (MIT 6.041SC)

by John Tsitsiklis · MIT OpenCourseWare

Modeling and analysis of uncertainty: probability models, discrete and continuous random variables, Bayesian inference, limit theorems and random processes. Designed for independent study, with lecture videos, slides, recitation and tutorial problems, problem sets and exams with solutions, and TA problem-solving videos.

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Introduction to Probability

Learn the fundamentals of probability with this introductory book by Blitzstein & Hwang. Perfect for statistics beginners!

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probabilitycourse.com

ProbabilityCourse.com is an online learning resource that provides a structured probability course with clear explanations, worked examples, and practice problems covering topics from basics to advanced theory.

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seeing-theory.brown.edu

Seeing Theory is an interactive, browser-based resource from Brown University that uses visual simulations to explain fundamental probability and statistics concepts. It offers interactive demos and explanations on topics like probability, distributions, sampling, the central limit theorem, confidence intervals, hypothesis testing, and Bayesian reasoning.

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Bayes Theorem, the geometry of changing beliefs

Grant Sanderson builds Bayes' theorem from a diagram of overlapping populations rather than the formula, using the medical-test and Steve-the-librarian examples. Viewers finish able to reason about how evidence should shift a prior probability.

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Information Theory (MIT 6.441)

Graduate introduction to the mathematics of information: entropy, lossless compression, binary hypothesis testing, channel coding and lossy compression. Provides 29 lecture note files that together form a textbook-length treatment, plus problem sets. Prepares you to state and prove the core coding theorems.

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Binomial distributions | Probabilities of probabilities, part 1

Animated walkthrough of the binomial distribution, using a product-review example to show how observed successes and failures translate into a probability density over an unknown underlying success rate. Explains where the binomial coefficient comes from.

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