Probabilistic Systems Analysis and Applied Probability
MIT's 6.041/6.431 covers the modeling and analysis of random phenomena, building from basic probability laws up through Bayesian inference, Markov chains, and limit theorems. The course works through discrete and continuous random variables, expectation and variance, conditional probability, and the weak law of large numbers, before ending with an introduction to statistical inference and hypothesis testing. Materials include full video lectures, lecture notes, problem sets with solutions, and exams with solutions, published through MIT OpenCourseWare. The course is designed for students with a calculus background and is used as MIT's core probability class for electrical engineering and computer science majors. No certificate is offered, but all materials are free to access and reuse under a Creative Commons license.