Probability Calculus II 360-MS1-3RP2a
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
Type of course
Prerequisites (description)
Course coordinators
Term 2022: | Term 2023: |
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 criteria
The overall form of credit for the course: final exam
Additional information
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: