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. This course is part of a MicroMasters® Program.
The Probability - The Science of Uncertainty and Data certificate at Massachusetts Institute of Technology - MITx, part of the MITx MicroMasters Program in Statistics and Data Science 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)
What you'll learn:
- The basic structure and elements of probabilistic models
- Random variables, their distributions, means, and variances
- Probabilistic calculations
- Inference methods
- Laws of large numbers and their applications
- Random processes
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Visit programme websiteProgramme Structure
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
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Visit programme websiteKey information
Duration
- Part-time
- 4 months
- 10 hrs/week
Start dates & application deadlines
Language
Delivered
Disciplines
Mathematics Data Science & Big Data View 53 other Short Courses in Mathematics in United StatesExplore more key information
Visit programme websiteAcademic requirements
We are not aware of any specific GRE, GMAT or GPA grading score requirements for this programme.
English requirements
We are not aware of any English requirements for this programme.
Other requirements
General requirements
Prerequisites:
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.
Make sure you meet all requirements
Visit programme websiteTuition Fee
-
International
300 USD/fullTuition FeeBased on the tuition of 300 USD for the full programme during 4 months. -
National
300 USD/fullTuition FeeBased on the tuition of 300 USD for the full programme during 4 months.
- Add a Verified Certificate for $300 USD
- Limited access:free