Probability Calculus II
General data
Course ID:  360MS13RP2a 
Erasmus code / ISCED: 
11.102

Course title:  Probability Calculus II 
Name in Polish:  Probability Calculus II 
Organizational unit:  Faculty of Mathematics 
Course groups: 
(in Polish) Erasmus+ sem. letni 
ECTS credit allocation (and other scores): 
4.00

Language:  English 
Type of course:  elective courses 
Prerequisites (description):  Student should know basic methods from mathematical analysis and Probability Calculus I. 
Short description: 
Course profile: academic Form of study: stationary Academic discipline: science and natural science, field of study in the arts and science: mathematics Prerequisities: Mathematical Analysis, Probablility Calculus I lecture 30 h. exercise class 30 h. ECTS credits: 4 
Full description: 
Course is devoted to probabilistic methods in theory and applications. After course students should know basic methods and theorems in random variables, conditional expected value, characteristic functions, limit theorems and stochastic processes. Topics: 1. Random variables and their distributions 2. Conditional expected value 3. Characteristic functions for random variables 4. Sequences of random variables and their distributions 5. Central limit theorem 6. Elements of stochastic processes 7. Markov chains 8. Wiener stochastic process and Ito integral Verification methods: lectures, exercises, consultations, studying literature, home works, discussions in groups. Balance of student workload: attending lectures15x2h = 30h attending exercise classes 15x2h = 30h preparation for classes 7x3h = 21h completing notes after exercises and lectures 7x2h = 14h consultations 12x1h = 12h the final examination: preparation.and take 12h + 3h = 15h control works: repeating the material and preparation 3x4h = 12h Quantitative description Direct interaction with the teacher: 75 h., 3 ECTS 
Bibliography: 
1. H. Tucker A graduate Course in Probablility, Dover Publ. 2014 2. T. Brzeźniak, T. Zastawniak Basic Stochastic Processes. A course through exercises, Springer 1999 3. M. Capiński, E. Kopp, Measure, Integral and Probability, Springer 2004 4. P. Billingsley Probability and Measure, Willey 2012 
Learning outcomes: 
Learning outcomes: Student knows probability distributions of basic random variables, such as normal distribution, gamma distribution, Poisson distribution etc. Student knows theorems and properties of convergence of sequences of random variables. Student understand the notion of conditional expected value and uses it in practise Student knows characteristic functions for basic probability distributions and their properties Student knows Central Limit Theorem and uses it in practise Student understand the notion of Markov chain, knows classification of states in Markov chain and calculates probabilities of states. Student understand the notion of Wiener process and calculates Ito integral. 
Assessment methods and assessment criteria: 
The overall form of credit for the course: final exam 
Classes in period "Academic year 2022/2023" (past)
Time span:  20221001  20230630 
Navigate to timetable
MO TU WYK
CW
W TH FR 
Type of class: 
Class, 30 hours
Lecture, 30 hours


Coordinators:  Tomasz Czyżycki, Urszula Ostaszewska, Aneta Sliżewska  
Group instructors:  Urszula Ostaszewska  
Students list:  (inaccessible to you)  
Examination: 
Course 
Examination
Class  Grading 

Short description: 
Course profile: academic Form of study: stationary Academic discipline: Mathematics, field of study in science: mathematics Prerequisities: Mathematical Analysis, Probablility Calculus I lecture 30 h. exercise class 30 h. ECTS credits: 4 

Full description: 
Course is devoted to probabilistic methods in theory and applications. After course students should know basic methods and theorems in random variables, conditional expected value, characteristic functions, limit theorems and stochastic processes. Topics: 1. Random variables and their distributions 2. Conditional expected value 3. Characteristic functions for random variables 4. Sequences of random variables and their distributions 5. Central limit theorem 6. Elements of stochastic processes 7. Markov chains 8. Wiener stochastic process and Ito integral Verification methods: lectures, exercises, consultations, studying literature, home works, discussions in groups. Balance of student workload: attending lectures15x2h = 30h attending exercise classes 15x2h = 30h preparation for classes 7x3h = 21h completing notes after exercises and lectures 7x2h = 14h consultations 12x1h = 12h the final examination: preparation.and take 12h + 3h = 15h control works: repeating the material and preparation 3x4h = 12h Quantitative description Direct interaction with the teacher: 75 h., 3 ECTS 

Bibliography: 
1. H. Tucker A graduate Course in Probablility, Dover Publ. 2014 2. T. Brzeźniak, T. Zastawniak Basic Stochastic Processes. A course through exercises, Springer 1999 3. M. Capiński, E. Kopp, Measure, Integral and Probability, Springer 2004 4. P. Billingsley Probability and Measure, Willey 2012 
Classes in period "Academic year 2023/2024" (past)
Time span:  20231001  20240630 
Navigate to timetable
MO WYK
TU CW
W TH FR 
Type of class: 
Class, 30 hours
Lecture, 30 hours


Coordinators:  Urszula Ostaszewska  
Group instructors:  Urszula Ostaszewska  
Students list:  (inaccessible to you)  
Examination: 
Course 
Examination
Class  Grading 

Short description: 
Course profile: academic Form of study: stationary Academic discipline: Mathematics, field of study in science: mathematics Prerequisities: Mathematical Analysis, Probablility Calculus I lecture 30 h. exercise class 30 h. ECTS credits: 4 

Full description: 
Course is devoted to probabilistic methods in theory and applications. After course students should know basic methods and theorems in random variables, conditional expected value, characteristic functions, limit theorems and stochastic processes. Topics: 1. Random variables and their distributions 2. Conditional expected value 3. Characteristic functions for random variables 4. Sequences of random variables and their distributions 5. Central limit theorem Verification methods: lectures, exercises, consultations, studying literature, home works, discussions in groups. Balance of student workload: attending lectures15x2h = 30h attending exercise classes 15x2h = 30h preparation for classes 7x3h = 21h completing notes after exercises and lectures 7x2h = 14h consultations 12x1h = 12h the final examination: preparation.and take 12h + 3h = 15h control works: repeating the material and preparation 3x4h = 12h Quantitative description Direct interaction with the teacher: 75 h., 3 ECTS 

Bibliography: 
1. H. Tucker A graduate Course in Probablility, Dover Publ. 2014 2. T. Brzeźniak, T. Zastawniak Basic Stochastic Processes. A course through exercises, Springer 1999 3. M. Capiński, E. Kopp, Measure, Integral and Probability, Springer 2004 4. P. Billingsley Probability and Measure, Willey 2012 
Classes in period "Academic year 2024/2025" (future)
Time span:  20241001  20250630 
Navigate to timetable
MO TU W TH FR 
Type of class: 
Class, 30 hours
Lecture, 30 hours


Coordinators:  (unknown)  
Group instructors:  Urszula Ostaszewska  
Students list:  (inaccessible to you)  
Examination: 
Course 
Examination
Class  Grading 
Copyright by University of Bialystok.