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September 21, 2023

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Description

6.041/6.431 Probabilistic Systems Analysis and Applied Probability (Fall 2010, MIT OCW). Instructor: Professor John Tsitsiklis.

Welcome to 6.041/6.431, a subject on the modeling and analysis of random phenomena and processes, including the basics of statistical inference. Nowadays, there is broad consensus that the ability to think probabilistically is a fundamental component of scientific literacy. The aim of this course is to introduce the relevant models, skills, and tools, by combining mathematics with conceptual understanding and intuition. (from ocw.mit.edu)

Course Curriculum

  • Lecture 01 – Probability Models and Axioms Unlimited
  • Lecture 02 – Conditioning and Bayes’ Rule Unlimited
  • Lecture 03 – Independence Unlimited
  • Lecture 04 – Counting Unlimited
  • Lecture 05 – Discrete Random Variables; Probability Mass Function; Expectations Unlimited
  • Lecture 06 – Discrete Random Variable Examples; Joint PMFs Unlimited
  • Lecture 07 – Multiple Discrete Random Variables; Expectations, Conditioning, Independence Unlimited
  • Lecture 08 – Continuous Random Variables Unlimited
  • Lecture 09 – Multiple Continuous Random Variables Unlimited
  • Lecture 10 – Continuous Bayes’ Rule; Derived Distributions Unlimited
  • Lecture 11 – Derived Distributions; Convolution; Covariance and Correlation Unlimited
  • Lecture 12 – Iterated Expectations; Sum of a Random Number of Random Variables Unlimited
  • Lecture 13 – Bernoulli Process Unlimited
  • Lecture 14 – Poisson Process I Unlimited
  • Lecture 15 – Poisson Process II Unlimited
  • Lecture 16 – Markov Chains I Unlimited
  • Lecture 17 – Markov Chains II Unlimited
  • Lecture 18 – Markov Chains III Unlimited
  • Lecture 19 – Weak Law of Large Numbers Unlimited
  • Lecture 20 – Central Limit Theorem Unlimited
  • Lecture 21 – Bayesian Statistical Inference I Unlimited
  • Lecture 22 – Bayesian Statistical Inference II Unlimited
  • Lecture 23 – Classical Statistical Inference I Unlimited
  • Lecture 24 – Classical Inference II Unlimited
  • Lecture 25 – Classical Inference III; Course Overview Unlimited

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