Probability and Statistics
Probability and Statistics
Data is displayed for the academic year: 2025./2026.
Course Description
We introduce and investigate the probability spaces, discrete and continuous random variables and discrete random vectors. Main discrete and continuous random variables are studied. We introduce the basics of sampling theory and learn how to implement some statistical tests.
Study Programmes
undergraduate
Chemical, Biological, Radiological and Nuclear Defence - course
(3. semester)
Group of Courses Signals, Monitoring and Guidance and Air Defence - course
(3. semester)
Learning Outcomes
- explain and interpret basic concepts from the course (probability, random variable, numerical characteriistic of random variable).
- outline basic definitions and statements of main theorems.
- illustrate problem by mathematical model and apply appropriate mathematical method
- apply fundamental statistic tests in practical problems in statistics.
- demonstrate fundamental skills contained in the course.
- apply mathematical reasoning adequately.
Forms of Teaching
Lectures
Lectures with a large number of example and problems
ExercisesMore examples for students work
Independent assignmentsFrom workbook
Week by Week Schedule
- Lectures: Probability Space. Finite Probability space. Fundamentals of Combinatorics. Exercises: Finite Probability Space. Fundamentals of Combinatorics.
- Lectures: Discrete Infinite Probability Space. Geometrical Probability. Exercises: Fundamentals of Combinatorics. Discrete Infinite Probability Space. Geometrical Probability.
- Lectures: Conditional Probability. Independence. Exercises: Conditional Probability. Independence.
- Lectures: Discrete Random Variables. Probability Distribution. Mathematical Expectation and Variance. Exercises: Discrete Random Variables. Probability Distribution. Mathematical Expectation and Variance.
- Lectures: Discrete Random Vectors. Covariance and Correlation. Exercises: Discrete Random Vectors. Covariance and Correlation.
- Lectures: Binomial, Geometric and Poisson Distribution. Exercises: Binomial, Geometric and Poisson Distribution.
- Lectures: Continuous Random Variables. Probability Density. Exercises: Continuous Random Variables. Probability Density.
- Lectures: Exponential and Normal Distribution. Normal Approximation to the Binomial and Poisson Distribution. Exercises: Exponential and Normal Distribution. Normal Approximation to the Binomial and Poisson Distribution.
- Lectures: The Laws of Large Numbers. The Central Limit Theorem. Exercises: The Laws of Large Numbers. The Central Limit Theorem.
- Lectures: Descriptive Statistic. Exercises: Descriptive Statistic.
- Lectures: Point Estimations. Linear Regression. Exercises: Point Estimations. Linear Regression.
- Lectures: Estimations by Confidence Intervals. Exercises: Estimations by Confidence Intervals.
- Lectures: Tests of Hypotheses for a Single Sample. Exercises: Tests of Hypotheses for a Single Sample.
- Lectures: Statistical Inference for Two Samples. Exercises: Statistical Inference for Two Samples.
- Lectures: Chi-Square Goodness-of-Fit Test. Exercises: Chi-Square Goodness-of-Fit Test.
Literature
Neven Elezović (2008.), Diskretna vjerojatnost, Element
Neven Elezović (2008.), Slučajne varijable, Element
Neven Elezović (.), Statistika i procesi, Element
Slavka Pfaff (2012.), Osnove statistike, Element
Iva Franjić, Ana Vukelić (.), nastavni materijali na webu (http://www.pbf.unizg.hr/hr/zavodi/zavod_za_procesno_inzenjerstvo/kabinet_za_matematiku/biostatistika_studij_nutricionizam/nastavni_materijali/predavanja_i_seminari),
For students
General
ID 282341
Winter semester
5.0 ECTS
L0 English Level
L1 e-Learning
30 Lectures
30 Exercises