- basic concepts of probability theory (probability space, random variable, distribution),
- distribution of real-valued random variables (binomial, Poisson, exponential and normal distribution, etc.),
- expected value, variance, covariance,
- distribution of random vectors, multivariate normal distribution as an example,
- conditional probability, independence,
- law of large numbers,
- central limit theorem.
Fundamentals of statistics:
- parameter estimator,
- interval estimator,
Outlook on the following areas:
- Monte Carlo simulation,
- linear regression,
- big data and machine learning,
- Markov chains.