FAKULTETA ZA GRADBENIŠTVO, PROMETNO INŽENIRSTVO IN ARHITEKTURO


Subject
 STATISTICS 
https://aips.um.si/PredmetiBP5/UcnaEnotaInfo.asp?Zavod=16&Jezik=A&Leto=2017&Nacin=&Predmet=58V314

Study unit code    58V314 2017

Level Study program or it's part Year Semester
2 BV2C MODULE ROAD TRAFFIC 2 Winter
2 BV2Ž MODULE RAILWAY TRAFFIC 2 Winter

ECTS kredits 3

Hours - Lectures 25
Hours - Tutorial 20
Hours - Individual Student's Work 45

Lecturers
doc. dr. ERVEŠ RIJA

Languages - lectures slovene
Languages - tutorial slovene

Prerequisits
Knowledge of Mathematics I and Mathematics II courses. 
Content (Syllabus outline)
Data processing and sampling: sampling, sorting, grouping, tables, graphical representationes (histograms), median, quartiles, interquartile range, average, variance and standard deviation. Events, experiments: experiments and events, random variables, population, sampling. Algebra of events: elementary events and composed events, certain and impossible event, operations on events, Boolean algebra. Probability: definition of probability, probability of composed events, addition rule for muttually exclusive events, addition rule for arbitrary events, probability as a measure on the algebra of events. Conditional probability: definition of conditional probability, independent events, multiplication rule, relay experiments and Bayes formula. Permutations and combinations: permutation of given things (the number of places equals to the number of things, the number of places differs from the number of things), permutation of different things which are divided into different classes (sets), permutation with repetitions, combinations without repetitions, combinations with repetitions, binomial coefficients, Stirling formula. Probability distributions: Discrete and continuous distributions, probability density and distribution of discrete and continuos random variable. Mean value and variance: mean and variance of discrete (or continuous) random variables, normalization, moments. Binomial, Poisson and hipergeometric distribution, normal distribution, distributive function of normal distribution, standardization of normal distribution, table of standard normal distribution. Random vectors (multi-dimensional distributions): discrete multi-dimensional distributions, continuous multi-dimensional distributions, marginal distributions of discrete distribution, marginal distributions of continuous distribution, functions of random distribution, theorems on additivity and multiplicativity of mean value and variance additivity. Introduction to mathematical statistics: Statistics as application of probability calculus, basic concepts of statistics: population, sample, parameter estimation, statistical test, regression and correlation analyses, maximum likelihood method. Confidence intervals: Confidence intervals of mean value of normal distribution at known variance, sum of independent normal variables, confidence intervals of mean value of normal distribution at unknown variance, t-distribution, confidence interval for variance, chi-square distribution, confidence intervals for other distributions, central limit theorem. Testing of hypotheses: Statistical test, types of alternatives, types of errors in tests, test for mean value of normal distribution at known variance, test for mean value of normal distribution at unknown variance, normal distribution variance test, comparison of mean values of two normal distributions, comparison of variances of two normal distributions Quality control: quality control description, mean value diagram, variance diagram, standard deviation control diagram, control diagram of extreme values Acceptance test: Acceptance test description, acceptance test errors, and rejections. Adjustment test (chi-square test): testing of the distribution function type, examples of chi-square test. Nonparametric tests: median test, trend test. Regression analysis (linear connection adjustment): problem description – connection between a non-random and random variable, method of least squares, confidence interval in regression analysis. Correlation analysis: Description of a problem – connection between two random variables, correlation coefficient, sample correlation coefficient, independence and non-correlation, correlation coefficiency test Theory of series: absolutely and conditionally convergent series, calculation operations with series, exponent series, Taylor serie. Time series: The analysis of time series, smoothing, estimation of trend, modelling of random processes (ARIMA models), forecasting.  
Readings
Svitan Gaborovič, Statistika, FG v pripravi dodatna literature: Rajko Jamnik, Verjetnostni račun in statistika, Društvo matematikov, fizikov in astronomov Slovenije, Ljubljana 1986, 154 str. Mališić, Jovan D., Zbirka zadataka iz teorije verovatnoče sa primenama, Beograd : Graevinska knjiga, 1990, 296 str. Dodatno: Erwin Kreyszig, Advanced Engeneering Mathematics, John Wiley & Sons, Inc. 1999 Rajko Jamnik, Verjetnostni raˇcun, Mladinska knjiga, 1987, 275 str. Rajko Jamnik, Matematična statistika, Državna založba Slovenije, 1980, 408 str. Murray R. Spiegel, Statistics, ,Shaum‘s outline series, McGraw Hill, New York, 1961, 359 str. Peter J. Brockwell, Richard A. Davis, Introduction to Time Series and Forecasting, Springer, 2002, 435 str. + CD 
Objectives and competences
Student have to skilled in using statistical methods when solving profesional problems.  
Intended learning outcomes - knowledge and understanding
The student have to understand the notion of randomness and probability, know the most important distributions from statistics, be able to estimate reliability of data given by experiments (measurements), know to calculate confidence intervals, know to check reliability of hypothesis that are based on experiments (hypothesis concerning parameters ot type of distribution), and know to calculate parameters using maximul likelihood method. 
Intended learning outcomes - transferable/key skills and other attributes
The student have to understand the notion of randomness and probability, to estimate reliability of data given by experiments (measurements), know to check reliability of hypothesis that are based on experiments. 
Learning and teaching methods
 

Assessment Weight (%)
Oral examination 40  
Written examination 60  
[EOP]