Probability theory 1000-213bRP

- Probability space: axioms of probability; properties of probability spaces; classical definition of probability; probability measures.
- Conditional probability and independence: definition of conditional probability, Law of Total Probability, Bayes' Theorem, independence of events.
- Discrete random variables: definition, properties, basic probability distributions - two-point, binomial, Poisson, geometric.
- Basic probability distributions: Bernoulli, binomial, Poisson, geometric, normal, exponential
- Parameters of probability distributions: expected value, variance, higher moments.
- Inequalities and limit theorems: Markov Inequality, Chebyshev Inequality, Law of Large Numbers, Central Limit Theorem.
- Continuous random variables: definition, properties, exponential and normal distributions,
- Markov chains: definition and basic properties, classification of states, ergodicity, applications.