### Popis predmeta

#### Course Description

In the introductory chapter, the generation of pseudorandom numbers will be studied. The properties of the most important types of distributions occurring in engineering are studied and the models in which they occur are examined. These models are simulated using a computer. Similar techniques is used in modelling finite Markov chains and the Poisson process. The Monte Carlo method is studied. Finally, the problem of variance reduction in sampling is addressed.

#### Learning Outcomes

1. Improve knowledge about the basic laws of random events
2. Learn to distinguish the most important random variables according to their properties
3. Model important distributions
4. Model complex situations in which randomness occurs
5. Model stochastic processes and Markov chains
6. Apply the basic techniques of the Monte Carlo method

#### Forms of Teaching

Lectures

Seminars and workshops

Independent assignments

#### Week by Week Schedule

1. Pseudorandom number generators, Statistical analysis of simulated data
2. The sample mean and sample variance, Interval estimates of a population mean, Goodnes of fit test
3. The inverse transform method, Poisson distribution
4. Bbinomial distribution, Geometric distribution, Negative binomial distribution, Hypergeometric distribution
5. The inverse transform algorithm, The polar method for genetrating normal random variables
6. Generatring random vectors, Multinormal distribution
7. Exponential distribution, Cauchy distribution, Gama and beta distributions, Weibul distribution
8. Midterm exam
9. Normal distribution, Lognormal distribution, Chi-square distribution, Student t-distribution, F distribution
10. Finite Markov chain, First exit time
11. Generating a Poisson process, Generating a nonhomogeneous Poisson process
12. Using random nubers to evaluate integrals, The sample mean Monte Carlo methods, Monte Carlo methods for linear systems
13. Importance sampling, Correlated sampling, Stratisfied sampling, Biased estimators
14. Seminar
15. Final exam

#### Study Programmes

Audio Technologies and Electroacoustics (profile)
Free Elective Courses (1. semester) (3. semester)
Communication and Space Technologies (profile)
Free Elective Courses (1. semester) (3. semester)
Computational Modelling in Engineering (profile)
Elective Courses of the Profile (3. semester) Free Elective Courses (1. semester)
Computer Engineering (profile)
Free Elective Courses (1. semester) (3. semester)
Computer Science (profile)
Free Elective Courses (1. semester) (3. semester)
Control Systems and Robotics (profile)
Free Elective Courses (1. semester) (3. semester)
Data Science (profile)
Free Elective Courses (1. semester) (3. semester)
Electrical Power Engineering (profile)
Free Elective Courses (1. semester) (3. semester)
Electric Machines, Drives and Automation (profile)
Free Elective Courses (1. semester) (3. semester)
Electronic and Computer Engineering (profile)
Free Elective Courses (1. semester) (3. semester)
Electronics (profile)
Free Elective Courses (1. semester) (3. semester)
Information and Communication Engineering (profile)
Free Elective Courses (1. semester) (3. semester)
Network Science (profile)
Elective Courses of the Profile (1. semester) (3. semester)
Software Engineering and Information Systems (profile)
Free Elective Courses (1. semester) (3. semester)

#### Literature

(.), Neven Elezović, Stohastičko modeliranje - skripta,
(.), Nedžad Limić, Monte Carlo simulacije slučajnih veličina, nizova i procesa, Zagreb, Element 2002,,
(.), M. A. Pinsky, S. Karlin, An Introduction to Stochastic Modeling, Elsevier 2011,
(.), S. M. Ross, Introduction to Probability Models, 10th ed., Elsevier 2010,

#### General

ID 222785
Winter semester
5 ECTS
L3 English Level
L1 e-Learning
45 Lectures

#### Learning Outcomes

1. Improve knowledge about the basic laws of random events
2. Learn to distinguish the most important random variables according to their properties
3. Model important distributions
4. Model complex situations in which randomness occurs
5. Model stochastic processes and Markov chains
6. Apply the basic techniques of the Monte Carlo method

#### Forms of Teaching

Lectures

Seminars and workshops

Independent assignments

#### Week by Week Schedule

1. Pseudorandom number generators, Statistical analysis of simulated data
2. The sample mean and sample variance, Interval estimates of a population mean, Goodnes of fit test
3. The inverse transform method, Poisson distribution
4. Bbinomial distribution, Geometric distribution, Negative binomial distribution, Hypergeometric distribution
5. The inverse transform algorithm, The polar method for genetrating normal random variables
6. Generatring random vectors, Multinormal distribution
7. Exponential distribution, Cauchy distribution, Gama and beta distributions, Weibul distribution
8. Midterm exam
9. Normal distribution, Lognormal distribution, Chi-square distribution, Student t-distribution, F distribution
10. Finite Markov chain, First exit time
11. Generating a Poisson process, Generating a nonhomogeneous Poisson process
12. Using random nubers to evaluate integrals, The sample mean Monte Carlo methods, Monte Carlo methods for linear systems
13. Importance sampling, Correlated sampling, Stratisfied sampling, Biased estimators
14. Seminar
15. Final exam

#### Study Programmes

Audio Technologies and Electroacoustics (profile)
Free Elective Courses (1. semester) (3. semester)
Communication and Space Technologies (profile)
Free Elective Courses (1. semester) (3. semester)
Computational Modelling in Engineering (profile)
Elective Courses of the Profile (3. semester) Free Elective Courses (1. semester)
Computer Engineering (profile)
Free Elective Courses (1. semester) (3. semester)
Computer Science (profile)
Free Elective Courses (1. semester) (3. semester)
Control Systems and Robotics (profile)
Free Elective Courses (1. semester) (3. semester)
Data Science (profile)
Free Elective Courses (1. semester) (3. semester)
Electrical Power Engineering (profile)
Free Elective Courses (1. semester) (3. semester)
Electric Machines, Drives and Automation (profile)
Free Elective Courses (1. semester) (3. semester)
Electronic and Computer Engineering (profile)
Free Elective Courses (1. semester) (3. semester)
Electronics (profile)
Free Elective Courses (1. semester) (3. semester)
Information and Communication Engineering (profile)
Free Elective Courses (1. semester) (3. semester)
Network Science (profile)
Elective Courses of the Profile (1. semester) (3. semester)
Software Engineering and Information Systems (profile)
Free Elective Courses (1. semester) (3. semester)

#### Literature

(.), Neven Elezović, Stohastičko modeliranje - skripta,
(.), Nedžad Limić, Monte Carlo simulacije slučajnih veličina, nizova i procesa, Zagreb, Element 2002,,
(.), M. A. Pinsky, S. Karlin, An Introduction to Stochastic Modeling, Elsevier 2011,
(.), S. M. Ross, Introduction to Probability Models, 10th ed., Elsevier 2010,

#### General

ID 222785
Winter semester
5 ECTS
L3 English Level
L1 e-Learning
45 Lectures