Syllabus
Probability:
Axioms of probability, basic examples (discrete and continuous). Conditional probability, the law of total probability, Bayes' theorem.
Random discrete variables: expectation, variance, linearity of expectation and its use. Basic discrete distributions.
Continuous random variables: description using probability density function. Basic continuous distributions.
Independent random variables. Random vectors (marginal distribution). Covariance, correlation.
Laws of large numbers, basic inequalities (Markov, Chebyshev, Chernoff), Central limit theorem.
Statistics:
Point estimates: unbiased estimates, confidence intervals.
Hypothesis testing, significance level. Two-sample tests.
Test of goodness of fit, test of independence.
Nonparametric estimates.
Bayesian and Frequentists Approach. Maximum a posteriori method, Least mean square estimate.
Maximum-likelihood method. Bootstrap resampling.
Simulation, generation of random variables from a distribution. Monte Carlo simulation.
Informatively: Markov chains.
Annotation
Basic lecture on Probability and Statistics for students of computer science. Students will learn the basic methods and concepts of the probabilistic description of reality: probability, random variable, distribution function and its density, random vectors, laws of large numbers. The emphasis will be on understanding the principles and the ability to use them.
Students will also learn the basics of mathematical statistics with an emphasis on understanding the applicability and on practical usage using the R language.