# Probability - The Science of Uncertainty and Data

Closed
Course
en
English
160 h
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• From www.edx.org
• 16 Sequences
• Starts on May 14, 2023
• Ends on September 3, 2023

## Course details

### Syllabus

Unit 1: Probability models and axioms

• Probability models and axioms
• Mathematical background: Sets; sequences, limits, and series; (un)countable sets.

Unit 2: Conditioning and independence

• Conditioning and Bayes' rule
• Independence

Unit 3: Counting

• Counting

Unit 4: Discrete random variables

• Probability mass functions and expectations
• Variance; Conditioning on an event; Multiple random variables
• Conditioning on a random variable; Independence of random variables

Unit 5: Continuous random variables

• Probability density functions
• Conditioning on an event; Multiple random variables
• Conditioning on a random variable; Independence; Bayes' rule

Unit 6: Further topics on random variables

• Derived distributions
• Sums of independent random variables; Covariance and correlation
• Conditional expectation and variance revisited; Sum of a random number of independent random variables

Unit 7: Bayesian inference

• Introduction to Bayesian inference
• Linear models with normal noise
• Least mean squares (LMS) estimation
• Linear least mean squares (LLMS) estimation

Unit 8: Limit theorems and classical statistics

• Inequalities, convergence, and the Weak Law of Large Numbers
• The Central Limit Theorem (CLT)
• An introduction to classical statistics

Unit 9: Bernoulli and Poisson processes

• The Bernoulli process
• The Poisson process
• More on the Poisson process

Unit 10 (Optional): Markov chains

• Finite-state Markov chains
• Steady-state behavior of Markov chains
• Absorption probabilities and expected time to absorption

### Prerequisite

College-level calculus (single-variable & multivariable). Comfort with mathematical reasoning; and familiarity with sequences, limits, infinite series, the chain rule, and ordinary or multiple integrals.

### Instructors

John Tsitsiklis
Professor, Department of Electrical Engineering and Computer Science
MIT

Patrick Jaillet
Professor, Electrical Engineering and Computer Science
MIT

Dimitri Bertsekas
Professor, Electrical Engineering and Computer Science
MIT

Karene Chu
Digital Learning Scientist and Research Scientist
Massachusetts Institute of Technology

Qing He
Teaching Assistant
MIT

Eren Can Kizildag
Teaching Assistant
MIT

Jimmy Li
Teaching Assistant
MIT

Jagdish Ramakrishnan
Teaching Assistant
MIT

Katie Szeto
Teaching Assistant
MIT

Kuang Xu
Teaching Assistant
MIT

### Editor

MIT is a world-class educational institution where teaching and research — with relevance to the practical world as a guiding principle — continue to be its primary purpose.

MIT is independent, coeducational, and privately endowed. Its five schools and one college encompass numerous academic departments, divisions and degree-granting programs, as well as interdisciplinary centers, laboratories and programs whose work cuts across traditional departmental boundaries.

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