- Improve knowledge about the basic laws of random events
- Learn to distinguish the most important random variables according to their properties
- Model important distributions
- Model complex situations in which randomness occurs
- Model stochastic processes and Markov chains
- Apply the basic techniques of the Monte Carlo method
Forms of Teaching
During lectures all the necessary results will be proved on the blackboard and immediately after that corresponding implementations will be done using computer (R programming language)Seminars and workshops
Seminars are optional, and allowed topics are anything related to the course material.Independent assignments
During the lectures, students will independently solve some tasks using computer and they will be rewarded in case of exceptional engagement. Furthermore, students will from time to time have some homework that they will have to solve using computer.
|Type||Threshold||Percent of Grade||Threshold||Percent of Grade|
|Homeworks||0 %||10 %||0 %||0 %|
|Seminar/Project||0 %||10 %||0 %||0 %|
|Mid Term Exam: Written||0 %||50 %||0 %|
|Final Exam: Written||0 %||50 %|
|Exam: Written||0 %||100 %|
Exams are written using a computer (typical problem is to write a code for some sort of simulation). Seminar and homework are optional for extra credit.
Week by Week Schedule
- Pseudorandom number generators. Statistical analysis of simulated data, goodness of fit tests.
- Inverse transformation method. Exponential distribution, logistic distribution, Cauchy distribution.
- General transformation methods, gamma distribution, chi-square distribution.
- Polar method (Box-Muller transform) for generating a normal random variable.
- Accept-reject method, beta distribution.
- Generation of discrete distributions. Geometric distribution.
- Binomial distribution, Poisson distribution.
- Midterm exam
- Introduction to Monte Carlo methods, use of random variables in the calculation of integrals.
- Importance sampling in Monte Carlo integration
- Simulating random walks.
- Using simulations of random walks in solving known problems from the theory of random processes.
- Simulating Brownian motion.
- Using simulations of Brownian motion in solving known problems from the theory of random processes.
- Final exam