The aim of studying and bibliography

The main aim of study:

The general information about the module:

Bibliography required to complete the module

Bibliography used during lectures

1	J. Jakubowski, R. Sztencel	Rachunek prawdopodobieństwa dla (prawie) każdego	Script, Warszawa.	2002
2	I.J. Diner i inni	Rachunek prawdopodobieństwa w problemach i zadaniach	PWN, Warszawa.	1979
3	T. Gestenkorn, T. Śródka	Kombinatoryka i rachunek prawdopodobieństwa	PWN, Warszawa.	1976
4	M.Startek	Podstawy rachunku prawdopodobieństwa z elementami statystyki matematycznej	Oficyna Wydawnicza PRZ.	2005
5	M. Fisz	Rachunek prawdopodobieństwa i statystyka matematyczna	PWN, Warszawa.	1969

Bibliography used during classes/laboratories/others

1	T. Gestenkorn, T. Śródka	Kombinatoryka i rachunek prawdopodobieństwa	PWN, Warszawa.	1976
2	W. Krysicki, J.Bartos, W. Dyczka, K. Królikowska, M. Wasilewskie	Rachunek prawdopodobieństwa i statystyka matematyczna w zadaniach, CZĘŚĆ I	PWN, Warszawa.	1999
3	J. Jakubowski, R. Sztencel,	Rachunek prawdopodobieństwa dla (prawie) każdego	Script, Warszawa,.	2002
4	A. Plucińska, E. Pluciński	Probabilistyka	WNT, Warszawa .	2000

Basic requirements in category knowledge/skills/social competences

Formal requirements: Student knows the mathematical analysis in the field that allows the use of differential and integral calculus of functions of one and many variables. The student satisfies the formal requirements set

Basic requirements in category knowledge:

Basic requirements in category skills:

Basic requirements in category social competences:

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 can create a probabilistic model and calculate the probability.	lecture, exercises	colloquium, exam	K_W01+ K_U02+ K_U04+ K_K01+ K_K02+ K_K05+	P6S_KK P6S_KO P6S_UW P6S_WG
02	Uses the expected value and other numerical characterizations of probabilistic processes.	lecture, exercises	colloquium, exam	K_W01+ K_U02+ K_U04+ K_K01+ K_K02+ K_K05+	P6S_KK 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
3	TK01	He models probabilistic experiences.	W1, C1	MEK01
3	TK02	Axiomatic and classic probability.	W2, C2	MEK01
3	TK03	Geometric probability.	W3, C3	MEK01
3	TK04	The conditional probability, a complete, Bayes' formula.	W4, C4	MEK01
3	TK05	Independence of events, Bernoulli's scheme.	W5, C5	MEK01
3	TK06	The distribution random variables.	W6, C6	MEK02
3	TK07	One-dimensional random variables (discrete).	W7, C7	MEK02
3	TK08	One-dimensional random variables (continuous)	W8, C8	MEK02
3	TK09	Expected value, variance, moments.	W9, C9	MEK02
3	TK10	Covariance, correlation coefficient.	W10, C10	MEK02
3	TK11	Multidimensional random variables.	W11, C11	MEK02
3	TK12	Distribution parameters, linear regression.	W12, C12	MEK02
3	TK13	Independent random variables.	W13, C13	MEK02
3	TK14	Conditional expected value.	W14, C14	MEK02
3	TK15	Limit theorems (Chebyshev inequality, law large numbers).	W15, C15	MEK02

The student's effort

The type of classes	The work before classes	The participation in classes	The work after classes
Lecture (sem. 3)		contact hours: 30.00 hours/sem.	complementing/reading through notes: 7.00 hours/sem. Studying the recommended bibliography: 15.00 hours/sem.
Class (sem. 3)	The preparation for a Class: 5.00 hours/sem.	contact hours: 30.00 hours/sem.	Finishing/Studying tasks: 10.00 hours/sem.
Advice (sem. 3)		The participation in Advice: 2.00 hours/sem.
Exam (sem. 3)	The preparation for an Exam: 16.00 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	Students who take two or more written tests obtained at least 50% of points will take the exam. A positive exam grade requires at least 50% of points to be awarded in a written exam.
Class	The condition for passing the tutorials is to obtain at least 50% of the points from the possible points on two written colloquia. Those who have passed the exam can take the written exam.
The final grade	The exam grade is the final grade of the module of education.

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