Class Central is learner-supported. When you buy through links on our site, we may earn an affiliate commission.

Online Course

Probability - The Science of Uncertainty and Data

Massachusetts Institute of Technology via edX

(3)
899
  • Provider edX
  • Cost Free Online Course (Audit)
  • Session Upcoming
  • Language English
  • Certificate $300 Certificate Available
  • Effort 10-14 hours a week
  • Duration 16 weeks long
  • Learn more about MOOCs

Taken this course? Share your experience with other students. Write review

Overview

The world is full of uncertainty: accidents, storms, unruly financial markets, noisy communications. The world is also full of data. Probabilistic modeling and the related field of statistical inference are the keys to analyzing data and making scientifically sound predictions.

Probabilistic models use the language of mathematics. But instead of relying on the traditional "theorem-proof" format, we develop the material in an intuitive -- but still rigorous and mathematically-precise -- manner. Furthermore, while the applications are multiple and evident, we emphasize the basic concepts and methodologies that are universally applicable.

The course covers all of the basic probability concepts, including:

  • multiple discrete or continuous random variables, expectations, and conditional distributions
  • laws of large numbers
  • the main tools of Bayesian inference methods
  • an introduction to random processes (Poisson processes and Markov chains)

The contents of this courseare heavily based upon the corresponding MIT class -- Introduction to Probability -- a course that has been offered and continuously refined over more than 50 years. It is a challenging class but will enable you to apply the tools of probability theory to real-world applications or to your research.

This course is part of theMITx MicroMasters Program in Statistics and Data Science. Master the skills needed to be an informed and effective practitioner of data science. You will complete this course and three others from MITx, at a similar pace and level of rigor as an on-campus course at MIT, and then take a virtually-proctored exam to earn your MicroMasters, an academic credential that will demonstrate your proficiency in data science or accelerate your path towards an MIT PhD or a Master's at other universities. To learn more about this program, please visit https://micromasters.mit.edu/ds/.

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

Taught by

John Tsitsiklis, Patrick Jaillet, Qing He, Jimmy Li, Jagdish Ramakrishnan, Katie Szeto, Kuang Xu, Dimitri Bertsekas and Eren Can Kizildag

Help Center

Most commonly asked questions about EdX

Reviews for edX's Probability - The Science of Uncertainty and Data Based on 3 reviews

  • 5 stars 100%
  • 4 star 0%
  • 3 star 0%
  • 2 star 0%
  • 1 star 0%

Did you take this course? Share your experience with other students.

Write a review
  • 1
Arnaud D
Arnaud is taking this course right now, spending 4 hours a week on it and found the course difficulty to be medium.
This is a great introducing course on probability. A certain level in math is a prerequisite, but nothing complicated. The teacher is clear and the his explanations really help to understand notion that can appear complicated at first glance. The exercices are designed to help the understanding. They're not "challenging", but are helpful.
Was this review helpful to you? Yes
Federico C
Federico is taking this course right now, spending 12 hours a week on it and found the course difficulty to be hard.
It is an introductory course but, I would not recommend it to somebody that doesn't have any idea of probability or statistics. The problems and exams have some difficult exercises. After taking many probability courses, this is the first time I feel I really understand it. It is fun and rigorous at the same. It is one of the best MOOC I've taken if not the best.
Was this review helpful to you? Yes
郭宇 郭
郭宇 completed this course, spending 40 hours a week on it and found the course difficulty to be medium.
It is the most valuable course I have ever attended. The lecture is not only understandable but also with rigorous proof. Thanks, it really helps!
Was this review helpful to you? Yes
  • 1

Class Central

Get personalized course recommendations, track subjects and courses with reminders, and more.

Sign up for free

Never stop learning Never Stop Learning!

Get personalized course recommendations, track subjects and courses with reminders, and more.

Sign up for free