After finishing the course successfully, students should be able to
- understand concepts of elementary probability theory and compute combinatorial probabilities, conditional probabilities and use independence.
- apply the probability distribution of one random variable and their characteristics, like expectation and variance, and can calculate probabilities and measures in practical examples.
- recognize and use basic distributions for numbers (discrete) and interval variables (continuous), among others the normal and binomial distribution and can apply them in described practical situations.
- apply probability theory on joint and conditional discrete variables, including the computation of correlation coefficient and determination of the distribution of a function of discrete and continuous variables.
- determine expectations and probabilities for sums and means of independent variables, especially for normally distributed variables and can apply the central limit theorem for large samples in case of binomial and other non-normal distributions
Sample space, event, axioms of Kolmogorov, combinatorial probability, conditional probability, Bayes’ rule, independence, random variable, expectation, variance, standard deviation, density, (cumulative) distribution function and distributions: binomial, hypergeometric, geometric, Poisson, exponential, uniform and normal, joint and conditional distributions, correlation, the distribution of the sum and the mean of independent variables, the Central Limit Theorem and its applications such as the normal approximation of binomial probabilities.