Introduction to Probability - The Science of Uncertainty
Solutions to MITx: 6.041x Introduction to Probability - The Science of Uncertainty https://www.edx.org/course/introduction-probability-science-mitx-6-041x-1
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 course are essentially the same as those of the corresponding MIT class (Probabilistic Systems Analysis and Applied Probability) -- a course that has been offered and continuously refined over more than 50 years. It is a challenging class, but it will enable you to apply the tools of probability theory to real-world applications or your research.