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Probability Theory
Major: Applied Mathematics
Code of Subject: 6.113.00.O.32
Credits: 5
Department: Applied Mathematics
Lecturer: DSc., Prof. Petro P. Kostrobij
Semester: 5 семестр
Mode of Study: денна
Learning outcomes:
• to know basic concepts, theorems, and methods of probability theory;
• to be able to construct mathematical models for description of random variables, random vectors and to investigate it.
• to be able to construct mathematical models for description of random variables, random vectors and to investigate it.
Required prior and related subjects:
Prerequisites:
• mathematical analysis,
• algebra and geometry,
• discrete mathematics,
• functional analysis;
Co-requisites:
• mathematical statistics,
• random processes.
• mathematical analysis,
• algebra and geometry,
• discrete mathematics,
• functional analysis;
Co-requisites:
• mathematical statistics,
• random processes.
Summary of the subject:
Random events, probability of random events, basic theorems. Repeated independent trials, Bernoulli scheme and its asymptotic. Random values and their description. Random vectors and their description. Sequences of random variables. Convergence. Limit theorems.
Recommended Books:
1. Pugachev V. S. Teorija verojatnostej i matematicheskaja statistika. – Moskva: Fiz. mat. lit., 2002, – 410 s.
2. Gihman I. I., Skorohod A. V., Jadrenko M. I. Teorija verojatnostej i matematicheskaja statistika. – K.: Vishha shkola, 1979. – 408 s.
3. Kostrobіj P. P. Teorіja jmovіrnostej. – L'vіv, 2016. – 259 s.
4. Efimov A. V. Sbornik zadach po matematike dlja vtuzov. Special'nye kursy. – Moskva: Nauka, 1984. – 608 s.
5. Metodichnі vkazіvki do vivchennja disciplіni "Teorіja jmovіrnostej" / Ukl.: P. P. Kostrobіj, O. V. Gajduchok, І. A. Saj. – L'vіv: Vidavnictvo Nacіonal'nogo unіversitetu "L'vіvs'ka polіtehnіka", 2010. – 83 s.
2. Gihman I. I., Skorohod A. V., Jadrenko M. I. Teorija verojatnostej i matematicheskaja statistika. – K.: Vishha shkola, 1979. – 408 s.
3. Kostrobіj P. P. Teorіja jmovіrnostej. – L'vіv, 2016. – 259 s.
4. Efimov A. V. Sbornik zadach po matematike dlja vtuzov. Special'nye kursy. – Moskva: Nauka, 1984. – 608 s.
5. Metodichnі vkazіvki do vivchennja disciplіni "Teorіja jmovіrnostej" / Ukl.: P. P. Kostrobіj, O. V. Gajduchok, І. A. Saj. – L'vіv: Vidavnictvo Nacіonal'nogo unіversitetu "L'vіvs'ka polіtehnіka", 2010. – 83 s.
Assessment methods and criteria:
• Current control (30%): surveys on practical classes, calculations, control works.
• Final control (70%): exam.
• Final control (70%): exam.
Probability Theory
Major: Applied mathematics and informatics
Code of Subject: 6.113.00.O.32
Credits: 5
Department: Applied Mathematics
Lecturer: DSc., Prof. Petro P. Kostrobij
Semester: 5 семестр
Mode of Study: денна
Learning outcomes:
• to know basic concepts, theorems, and methods of probability theory;
• to be able to construct mathematical models for description of random variables, random vectors and to investigate it.
• to be able to construct mathematical models for description of random variables, random vectors and to investigate it.
Required prior and related subjects:
Prerequisites:
• mathematical analysis,
• algebra and geometry,
• discrete mathematics,
• functional analysis;
Co-requisites:
• mathematical statistics,
• random processes.
• mathematical analysis,
• algebra and geometry,
• discrete mathematics,
• functional analysis;
Co-requisites:
• mathematical statistics,
• random processes.
Summary of the subject:
Random events, probability of random events, basic theorems. Repeated independent trials, Bernoulli scheme and its asymptotic. Random values and their description. Random vectors and their description. Sequences of random variables. Convergence. Limit theorems.
Recommended Books:
1. Pugachev V. S. Teorija verojatnostej i matematicheskaja statistika. – Moskva: Fiz. mat. lit., 2002, – 410 s.
2. Gihman I. I., Skorohod A. V., Jadrenko M. I. Teorija verojatnostej i matematicheskaja statistika. – K.: Vishha shkola, 1979. – 408 s.
3. Kostrobіj P. P. Teorіja jmovіrnostej. – L'vіv, 2016. – 259 s.
4. Efimov A. V. Sbornik zadach po matematike dlja vtuzov. Special'nye kursy. – Moskva: Nauka, 1984. – 608 s.
5. Metodichnі vkazіvki do vivchennja disciplіni "Teorіja jmovіrnostej" / Ukl.: P. P. Kostrobіj, O. V. Gajduchok, І. A. Saj. – L'vіv: Vidavnictvo Nacіonal'nogo unіversitetu "L'vіvs'ka polіtehnіka", 2010. – 83 s.
2. Gihman I. I., Skorohod A. V., Jadrenko M. I. Teorija verojatnostej i matematicheskaja statistika. – K.: Vishha shkola, 1979. – 408 s.
3. Kostrobіj P. P. Teorіja jmovіrnostej. – L'vіv, 2016. – 259 s.
4. Efimov A. V. Sbornik zadach po matematike dlja vtuzov. Special'nye kursy. – Moskva: Nauka, 1984. – 608 s.
5. Metodichnі vkazіvki do vivchennja disciplіni "Teorіja jmovіrnostej" / Ukl.: P. P. Kostrobіj, O. V. Gajduchok, І. A. Saj. – L'vіv: Vidavnictvo Nacіonal'nogo unіversitetu "L'vіvs'ka polіtehnіka", 2010. – 83 s.
Assessment methods and criteria:
• Current control (30%): surveys on practical classes, calculations, control works.
• Final control (70%): exam.
• Final control (70%): exam.