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- Basics of probability: Random experiment, sample space, axioms of probability, probability laws, Bayes’ theorem,
- Random variables and probability distributions (classical discrete and continuous probability distributions)
- Moments of random variables,
- Joint, marginal and conditional probability distributions
- Multivariate normal distribution,
- Moment-generating and characteristic functions,
- Convergence of sequence of random variables,
- Law of large numbers and central limit theorem;
- Sampling distribution;
- Point and interval estimation: characteristics of good estimator,
- Methods of estimation: Least squares and Maximum Likelihood estimation,
- Testing of hypothesis concerning means, variances and proportions
- Non-parametric tests: One sample and two sample tests
- Elements of generalized linear modeling.
- Application in R. (as a Master’s course in Data Sciences, we recommend that the lecturer should consider examples and problems from real life (with some data sets) and applications in the software R).
