STAT 200A: Applied Probability
This course is an introduction to probability theory, probability models and stochastic processes.
Basic concepts, axioms, measure theory.
One random variable, density, expectation, transformation, Lebesgue integral.
Two random variables, covariance, correlation, conditional distribution, conditional expectation and variance.
Three random variables, conditional independence.
Multivariate Gaussian distribution, diagonalization, conditional.
Law of large number, central limit theorem, large deviation.
Information theory: entropy and coding, Kullback-Leibler divergence.
Markov chains and Markov jump processes.
Brownian motion, stochastic differential equation, martingale.