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 independent 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).
Class 9 November 25, 2024
Poisson distribution. Normal distribution, it's significance, Central Limit
Theorem. Idea of a proof of the Central Limit Theorem using characteristic
function of a random variable and its properties (mainly according to Wikipedia:
Central limit theorem,
Characteristic function).
Class 10 December 2, 2024
Joint mass function, joint distribution function. Independent random
variables. If \(X\) and \(Y\) are indepenent random variables, then
\(E[XY] = E[X]E[Y]\). Covariance and correlation.
Class 11 December 9, 2024
Properties of correlation. Independent random variables are uncorrelated, but
not vice versa.
Datasets and their graphical representations.
Sample mean, sample variance, sample correlation (unbiased estimators).
Correlation is not causation.
Class 12 December 16, 2024
Statistical model, linear statistical model (linear regression), method of least
squares. Hypothesis testing, test statistic, null and alternative hypothesis,
\(p\)-value, type I and type II error.
A brief synopsis for this course at the previous semesters:
Created: Sun Sep 24 2017
Last modified: Tue Dec 17 2024 17:38:28 CET
