Probability Calculus II 360-MS1-3RP2a
Wykład (WYK) Rok akademicki 2022/23

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:

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.

The final exam will be oral.

For a satisfactory grade (3,0), the student is required to know the basic definitions and theorems.

For a grade of 4.0 and higher, knowledge of the proofs of theorems which were discussed during the lectures is required.

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

Teaching methods: lectures, exercises, consultations, studying literature, home works, discussions in groups.