The aim of studying and bibliography

The main aim of study: The aim of the module is to present the basics of stochastic processes.

The general information about the module: Typical stochastic processes and computer simulations of their.

Bibliography required to complete the module

Bibliography used during lectures

1	A. Plucińska, E. Pluciński	Rachunek prawdopodobieństwa. Statystyka matematyczna. Procesy stochastyczne.	WNT, Warszawa.	2009
2	J.F.C. Kingman	Procesy Poissona	PWN, Warszawa.	2002
3	M. Matalytski, O. Tikhonenko	Procesy stochastyczne	EXIT, Warszawa .	2011

Bibliography used during classes/laboratories/others

1

P. Biacek

Przewodnik po pakiecie R

Oficyna Wydawnicza GiS, Wrocław.

2017

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 method of probability.

Basic requirements in category skills: Knowledge of the method of probability, analysis and the R environment at the basic level.

Basic requirements in category social competences: Willingness to take objectively justified mathematical operations in order to solve the task .

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	He knows and can use the conditional expectation of random variable.	class, exercises	exam, test	K_W01++ K_U06+++	P6S_UW P6S_WG
02	He can describe some stochastic process..	class, exercises	exam, test	K_U06+++	P6S_UW
03	He can calcul the covarince of stochastic prcess.	class, exercisses	exam, test	K_W01++	P6S_WG
04	He can to form and analyse the model of random phenomenon.	Laboratory	Numerical analysys of simulation in R .	K_W02++ K_W04+++ K_U09+++ K_K05++	P6S_KO P6S_UW P6S_WG

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
6	TK01	Measurable space, measurable function. The continuity of measure with respect to anover measure.Random function, random element. Ϭ-field of random variable. Coditionel expectation of random variable.	W1-W12, C1-C12	MEK01
6	TK02	The term of stochastic process. Examples of stochastic processes.Applications of Poisson process and Winer process.Covariance of stochastic process. Markov process.	W13-W30, C13-C30	MEK02 MEK03
6	TK03	Simalations of random variables. Simulations of some models of stochastic processes. Parameters of stochastic prcesses.	L1-L5	MEK04
6	TK04	Constriction and analysys of some stochastic models of random phenomenon.	L6-L15

The student's effort

The type of classes	The work before classes	The participation in classes	The work after classes
Lecture (sem. 6)	The preparation for a test: 5.00 hours/sem.	contact hours: 30.00 hours/sem.	Studying the recommended bibliography: 8.00 hours/sem.
Class (sem. 6)	The preparation for a test: 10.00 hours/sem.	contact hours: 30.00 hours/sem.
Laboratory (sem. 6)		contact hours: 15.00 hours/sem.
Advice (sem. 6)		The participation in Advice: 1.00 hours/sem.
Exam (sem. 6)	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 and laboratory.
Class	Written test. The obvious exercises must be solved. Only the obvious exercises - 3.0.
Laboratory	On the base of simulation constructed in R.
The final grade	After the credit of all types of classes the final grade is the average of grade of classes, laboratory 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: no