Introduction, review of basic probability, and administrivia.
- The Kolmogorov axioms of probability theory; the definition of probability space (sample space, σ-algebra, probability measure); countable additivity and continuity of probability measures
- Fundamental building blocks: fair coin toss and standard unit-interval probability space
- Independence and conditional probability
- Random variables: definition; their distributions; functions of a random variable; probability density functions; some frequently used distributions
- Expectation of a random variable; properties of expectation (linearity, preservation of order, change of variables); characteristic functions
- Jointly distributed random variables: definition, examples, conditional densities and conditional expectations; transformations of random vectors