 Study

# Computing

## Probability and Statistics

• Class 60
• Practice 21
• Independent work 99
Total 180

### Course title

Probability and Statistics

Obligatory

183401

3

6

### Course objectives

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

### Prerequisites for:

1. Artificial Intelligence
2. Mobile Communications
3. Information Theory
4. Digital Video
5. Statistical Data Analysis

(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

#### Minimal learning outcomes

• Solve problems of evaluating probability of a given event
• Recognize specific discrete or continuous distribution
• Solve problems of evaluating expectation and variance of some distribution
• Analyze given data
• Solve problems of point and interval estimation
• Use statistical tests
• Demonstrate ability for mathematical modelling
• Use critical thinking