Theory of Probability

This course covers probability spaces as models for phenomena with statistical regularity. Students who take this course should be able to use the framework of probability to quantify uncertainty and update beliefs given the right evidence. Students will also learn how to use a variety of strategies to calculate probabilities and expectations, both conditional and unconditional, as well as how to understand the generative stories for discrete and continuous distributions and recognize when they are appropriate for real-world scenarios.

Topics Include

Naive and axiomatic definition of probability
Conditional probability such as Bayes' rule, independence of events and Simpson's paradox
Bernoulli, Binomial, and Hypergeometric distributions
Indicator r.v.s, continuous random variables and exponential distribution
Poisson distribution, approximation and process
Inequalities such as Cauchy-Schwarz, Jensen, Markov, Chebyshev and Chernoff