Probability - The Science of Uncertainty and Data

6.431x is MITx's probability course and part of the MicroMasters Program in Statistics and Data Science. It is based on MIT's long-running Introduction to Probability class and covers all the basic probability concepts: multiple discrete and continuous random variables, expectations and conditional distributions, laws of large numbers, the main tools of Bayesian inference, and an introduction to random processes including Poisson processes and Markov chains. The material is developed intuitively but with mathematical precision, rather than in a theorem-proof format, and the emphasis is on concepts and methods that apply universally even though the examples are wide-ranging. MIT describes it as a challenging class that prepares you to apply probability to real-world problems or research.

The course runs instructor-paced over an estimated 16 weeks; the catalogue lists 10 to 14 hours per week. Auditing is free and includes access to the course and materials. The certificate track costs $300 and provides graded assignments and exams plus an MIT certificate on completion, which can count toward the MicroMasters credential alongside the programme's other courses. The classroom counterpart, 6.041SC, is on OpenCourseWare without grading.