## Advanced Probability and Inference

## Content

- Mathematical background (limits, series, order relations and rates of convergence, continuity, sets)
- Measure theoretic foundations of probability (probability triplets, random variables, independence, expected values, change of variable)
- Stochastic convergence (almost sure convergence, convergence in probability, convergence in distribution, laws of large numbers, central limit theorems, non-iid stochastic variables)
- Conditional probability and expectation