Calendar description
Ensemble model of randomness. Conditional probability, independence, and Bayes' theorem. Random variables, probability distribution functions. Expected values. Collections of random variables, joint and marginal probability distributions, and correlation. Introduction to random processes. A detailed outline of the course can be found is here.
Pre-requisite: Discrete math and calculus.
Aims: This is the first in a sequence of two courses. This course concentrates mostly on probability theory. The second course will concentrate mostly on statistics.
Recommended reading
There is a course textbook. It is a well written book and well worth investing in. Obtaining a copy of the textbook, either a hard copy, or soft copy is recommended (albeit not strictly required).
- A First Course in Probability, (10th edition), Sheldon Ross, Pearson/Prentice-Hall, 2019.
There are many other good books that deal with the material. Some good examples are:
- Introduction to probability, D. P. Bertsekas and J. N. Tsitsiklis, Athena Scientific, 2002.
- Probability and Random Processes for Electrical Engineering, Albert Leon-Garcia, Pearson, 2007
- Probability, Random Variables and Stochastic Processes (4th Edition), A. Papoulis and S. U. Pillai, McGraw-Hill, 2002
Lecture material
- Introduction to probability: Axioms, sample spaces, events, and set operations. Sample spaces with equally likely outcomes.
- Independence and conditioning: Independence, conditional probabilities, law of total probability, Bayes' formula.
- Random variables and distributions: Expectation, moments, common distributions.
- Continuous Random Variables.
- Joint distributions and jointly distributed random variables: Joint distributions, sums of independent random variables, conditional distributions.
- Expectations and their properties: Moments, moment generating functions, characteristic functions, conditional expectation and its properties, jointly Gaussian random variables.
- Limit theorems: Probability inequalities, Central Limit Theorem (CLT), Weak Law of Large Numbers.