Short Course Description
Introduction to Probability
Prerequisites: Calculus 1 and 2, Linear algebra 1 and 2 (Calculus 2 and Linear Algebra 2 can be taken in parallel).
Short syllabus:
1. Finite and countable probability spaces, events and random variables, uniform probability spaces and combinatorics, union bound, inclusion-exclusion principle.
2. Conditional probability, chain rule, law of total probability, Bayes' law
3. Independence of events and random variables
4. Distributions of random variables, joint distribution, conditional distribution, distributions of functions of random variables, common distributions: Bernoulli, Binomial, uniform, geometric, hypergeometric, Poisson and other distributions.
5. Expectation and variance, conditional expectation and variance, covariance and correlation, Markov, Chebyshev and Jensen's inequalities.
6. Limit laws: law of large numbers, Poisson limit theorem, and the central limit theorem
7. Markov chains of finite state space: definition, periodicity and reducibility, stationary distribution and the convergence to the stationary distribution theorem.
Full syllabus will be available to registered students only
