# Probability and Statistics

##### Objectives and outcomes

Acquisition of general and specific knowledge in the field of Probability and Statistics. Upon completion
of the course, students will adopt the basic concepts, as well as the most important theorems in the field. Moreover, they will be able to apply the acquired knowledge to other courses.

##### Lectures

Basic concepts of probability theory and application of combinatorics. Conditional probability. Law of total
probability and the Bayes’ theorem. Random variables and random vectors. Independence of random
variables. Functions of random variables and random vectors. Numerical characteristics – mathematical
expectation, variance, normal distribution, moments, quantiles. Characteristic functions. Limit theorems
(law of large numbers and the central limit theorem). Distributions: Chi-square, Student’s distribution, F-
distribution Estimation of parameters. Hypothesis testing. Nonparametric tests. Monte Carlo methods.

##### Practical classes

Discrete probability spaces. Conditional and total probability. Important discrete distributions. Absolutely
continuous distributions (normal, uniform, exponential). Probability distribution function. Multidimensional
distribution function. Random variables. Mathematical expectation. Variance. Independence of random
variables. Covariance and correlation. Modelling of random quantities. Graphical display of data.
Population, trait, sample. Order statistics. Chi-square and other distributions important for statistical
modelling. Method of maximum likelihood. Confidence intervals. Statistical hypothesis testing.