### Probability and Statistics

#### Course Description

probability, conditional probability, discrete random variables and random vectors, continuous random variables and random vectors, limit theorems, descriptive statistics, point and interval estimations, statistical tests.

#### Learning Outcomes

1. solve problems of evaluating probability of a given event
2. recognize specific discrete or continuous distribution
3. solve problems of evaluating expectation and variance of some distribution
4. analyze given data
5. solve problems of point and interval estimation
6. use statistical tests
7. demonstrate ability for mathematical modelling
8. use critical thinking

#### Forms of Teaching

Lectures

4 hours per week

Exercises

1 hour per week

Independent assignments

each student must solve some problems on their own

Laboratory

6 hours per semester, 2 out of those 6 hours students work on their own

Continuous Assessment Exam
Type Threshold Percent of Grade Threshold Percent of Grade
Quizzes 0 % 10 % 0 % 10 %
Mid Term Exam: Written 0 % 50 % 0 %
Final Exam: Written 0 % 40 %
Exam: Written 0 % 90 %

#### Week by Week Schedule

1. Probability; equally likely outcomes; geometric probability
2. Conditional probability; independence; law of yotal probability; Bayes' rule
3. Discrete random variables and random vectors; marginal distribution; conditional distribution
4. Moments; characteristic function; generating functions
5. Geometric Distribution; Binomial Distribution; Poisson Distribution
6. Random variables; probability distributions; probablitiy densities, Functions of random variables
7. Exponential distribution; normal distribution
8. Midterm exam
9. Random vectors; conditional probability distributions
10. Functions of random vectors, Law of large numbers and central limit theorem
11. Measures of central tendency (mean, median, mode); measures of dispersion (standard deviation, variance, quantile, and IQR), Unbiased point estimations; Maximal-likelihood estimation
12. Interval estimations; confidence intervals, Confidence Intervals for parameters of normal distribution
13. Hypothesis testing; type of errors; parametric hypothesis testing; sampling distributions
14. Hypothesis testing; type of errors; parametric hypothesis testing; sampling distributions, Pearson's Chi-squared Test (Goodness-of-fit tests, tests of independence and homogeneity)
15. Final exam

#### Study Programmes

(3. semester)
(4. semester)
[FER2-HR] Computing - study
(4. semester)
[FER2-HR] Electrical Engineering and Information Technology - study
(4. semester)

#### Literature

(2018.), N.Elezović: Vjerojatnost i statistika, Element, Zagreb
(1989.), Ž. Pauše, Uvod u matematičku statistiku, Školska knjiga, Zagreb
(1989.), Ž. Pauše, Riješeni primjeri zadaci iz vjerojatnosti i statistike, Školska knjiga, Zagreb

#### General

ID 183401
Winter semester
6 ECTS
L1 English Level
L2 e-Learning
60 Lectures
0 Seminar
15 Exercises
6 Laboratory exercises
0 Project laboratory