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.