The aim of studying and bibliography

The main aim of study: Explore the basic messages and methods of probability.

The general information about the module: Probability, random variable, parameters of random variable, independence, sequences of random variables, limit theorems.

Bibliography required to complete the module

Bibliography used during lectures

1	M. Fisz	Rachunek prawdopodobieństwa i statystyka matematyczna	PWN, Warszawa.	1969
2	M. Startek	Podstawy rachunku prawdopodobieństwa z elementami statystyki matematycznej	Oficyna Wydawnicza Politechniki Rzeszowskiej.	2005
3	J. Stankiewicz, K. Wilczek	Elementy rachunku prawdopodobieństwa i statystyki matematycznej. Teoria, przykłady, zadania	Oficyna Wydawnicza Politechniki Rzeszowskiej.	2000

Bibliography used during classes/laboratories/others

1	M. Startek	Podstawy rachunku prawdopodobieństwa z elementami statystyki matematycznej	Oficyna Wydawnicza Politechniki Rzeszowskiej.	2005
2	W. Krysicki, J. Bartos, W. Dyczka, K. Królikowska, M. Wasilewski	Rachunek prawdopodobieństwa i statystyka matematyczna w zadaniach	WNT, Warszawa.	2003

Bibliography to self-study

1

A. i E. Plucińscy

Probabilistyka

WNT, Warszawa.

2003

Basic requirements in category knowledge/skills/social competences

Formal requirements: The student satisfies the formal requirements set out in the study regulations

Basic requirements in category knowledge: Knowing the analysis.

Basic requirements in category skills: Ability to use basic mathematical apparatus for the analysis.

Basic requirements in category social competences: The student is prepared to take substantially justified mathematical operations in order to solve the posed exercise.

Module outcomes

MEK	The student who completed the module	Types of classes / teaching methods leading to achieving a given outcome of teaching	Methods of verifying every mentioned outcome of teaching	Relationships with KEK	Relationships with PRK
01	use the concept of probability space, is able construct and analyze the mathematical model of random experiment;	lecture, classes	test, written exam	K_W01+ K_W03+ K_U30++	P6S_UW P6S_WG P6S_WK
02	is able to give examples of discrete and continuous probability distributions and discuss selected random experiment and mathematical models in which these distributions ocur; know the practical application of elementary distributions;	lecture, classes	test, written exam	K_W05+ K_U31++	P6S_UK P6S_UO P6S_UU P6S_UW P6S_WG
03	is able to use the formula of total probability and Bayes formula;	lecture, classes	test, written exam	K_W04+ K_U32++	P6S_UW P6S_WG P6S_WK
04	is able to count the parameters of distributions of random variables; is able to use limit theorems and the laws of large numbers.	lecture, classes	test, written exam	K_W02+ K_U33++ K_K01+	P6S_KK P6S_UW P6S_WG P6S_WK

Attention: Depending on the epidemic situation, verification of the achieved learning outcomes specified in the study program, in particular credits and examinations at the end of specific classes, can be implemented remotely (real-time meetings).

The syllabus of the module

Sem.	TK	The content	realized in	MEK
4	TK01	Genesis of probability. The sample space. Probability space. Properties of probability. Conditional probability, independence of events. The total probability, Bayes' theorem. Bernoulli trials. One- and n-dimensional random variables. Distribution function of random variable. Examples of discrete and continuous random variables. Correlation and regression. Sequences of random variables. Various types of convergences of random variables. The Tchebychev inequalit. The law of large numbers. The central limit theorem.	wykład, ćwiczenia	MEK01 MEK02 MEK03 MEK04

The student's effort

The type of classes	The work before classes	The participation in classes	The work after classes
Lecture (sem. 4)		contact hours: 30.00 hours/sem.	complementing/reading through notes: 15.00 hours/sem. Studying the recommended bibliography: 15.00 hours/sem.
Class (sem. 4)	The preparation for a Class: 15.00 hours/sem. The preparation for a test: 10.00 hours/sem. Others: 5.00 hours/sem.	contact hours: 30.00 hours/sem.	Finishing/Studying tasks: 20.00 hours/sem.
Advice (sem. 4)		The participation in Advice: 1.00 hours/sem.
Exam (sem. 4)	The preparation for an Exam: 10.00 hours/sem.	The written exam: 2.00 hours/sem.

The way of giving the component module grades and the final grade

The type of classes	The way of giving the final grade
Lecture	Written exam. The obvious exercises and the extra exercises. The obvious exercises must be solved. Only the obvious exercises - 3.0. Exam only after the credit of classes.
Class	Written test. The obvious exercises must be solved. Only the obvious exercises - 3.0.
The final grade	After the credit of all types of classes the final grade is the average of grade of classes and grade of exam.

Sample problems

Required during the exam/when receiving the credit
(-)

Realized during classes/laboratories/projects
(-)

Others
(-)

Can a student use any teaching aids during the exam/when receiving the credit : no

The contents of the module are associated with the research profile: yes

1	A. Linkov; E. Rejwer-Kosińska; L. Rybarska-Rusinek	The Study of Options for Identification Stress Contrasts via Pumping History	2023
2	A. Linkov; E. Rejwer-Kosińska; L. Rybarska-Rusinek	Evaluation of Rockburst Hazard by Accelerated Numerical Modeling of Stressed State and Induced Seismicity	2022
3	A. Linkov; E. Rejwer-Kosińska; L. Rybarska-Rusinek	On accuracy of translations by kernel independent fast multipole methods	2022
4	A. Linkov; E. Rejwer-Kosińska; L. Rybarska-Rusinek	On evaluation of local fields by fast multipole method employing smooth equivalent/check surfaces	2021
5	A. Linkov; E. Rejwer; L. Rybarska-Rusinek	On speeding up nano- and micromechanical calculations for irregular systems with long-range potentials	2020
6	L. Rybarska-Rusinek	On evaluation of influence coefficients for edge and intermediate boundary elements in 3D problems involving strong field concentrations	2019
7	L. Rybarska-Rusinek	Opracowanie metod i procedur numerycznych do modelowania obszarów o silnej koncentracji pól fizycznych	2019