All the books are available in electronic form in multiple places.
= available in
the university library
A BRIEF SYNOPSIS
(Each class lasted approximately 1.5 hours if not specified otherwise; tutorials
are running separately)
Class 1 September 23, 2024
Organizational issues. The subject of probability and statistics. A brief
refresher of combinatorics (permutations, variations without and with
repetitions, combinations, binomial coefficients).
Class 2 September 30, 2024
Inclusion-exlusion principle. Probabilistic terminology: sample space, event,
elementary event, examples. Definition of probability.
Class 3 October 7, 2024
Direct product of sample spaces. Examples of calculation of probabilities.
Inclusion-exclusion principle for probabilities. Conditional probability.
Bayes' formula and its generalization.
Class 4 October 14, 2024
Two ndependent events (equivalent definitions). Independence of a set of events.
Independence of events is not a transitive relation.
Class 5 October 21, 2024
Equivalence of two defintions of the independence of a set of events.
Notion of discrete random variable, mass function, and distribution function.
Examples. Properties of discrete distribution functions: piecewise constant,
non-decreasing, \(\lim_{x\to -\infty} F_X(x) = 0\),
\(\lim_{x\to +\infty} F_X(x) = 1\).
Class 6 November 4, 2024
Continuous random variable. Interplay between discrete and continuous.
Continuous distribution function, density function, its properties. Density is
not probability!
Definition of expectation, variance, and standard deviation of discrete and
continuous random variable.
Class 7 November 11, 2024
Alrernative formula for variance: \(Var(X) = E[X^2] - E[X]^2\).
Change of variables formulas for expectation and variance. Linear change of
variables.
Discrete unform distribution, its expectation and variance.
Class 8 November 18, 2024 Formulas for sums
of powers.
Continuous uniform distribution, binomal distribution, geometric distribution,
exponential distribution (definition, computation of expectation and variance
for each distribution).
A brief synopsis for this course at the previous semesters:
Created: Sun Sep 24 2017
Last modified: Mon Nov 18 2024 15:01:12 CET
