# Applied Statistics

## Course description

Basic concepts of probability: combinatorics (permutations, combinations, …), random variables (discrete, continuous) and their distributions (Gauss, Poisson, Weibull, …), numerical characteristics (expected value, variance).

Statistics: statistic design (definition of statistical hypothesis, sampling plans), data presentation, estimation of parameters (definition and properties of estimators), hypothesis testing (type one and type two error), confidence intervals, tests (parametric, non-parametric), regression and correlation (linear, bivariate, multivariate), time series (ARIMA, ARCH), simulations (Monte Carlo method).

## Objectives and competences

Grasp the basics of probability theory and statistical methods. Being able to collect and interpret statistical data and to make a critical analysis of the results and measurements in technical engineering with appropriately chosen statistical methods. Use of some statistical data analysis software.

## Learning and teaching methods

Lectures, laboratory work, homeworks, seminar assignment.

## Intended learning outcomes

After successful completion of the course, students should be able to:

• describe basic statistical methods used in technical engineering,
• distinguish between different  statistical methods,
• use statistical methods to make a statistical analysis,
• use statistical programming tools for solving statistical problems,
• critically analyse and statistically interpret technical problems that we encounter in practise,
• critically evaluate the solution.

## Reference nosilca

1. DOLINAR, Gregor, KUZMA, Bojan, NAGY, Gergő, SZOKOL, Patrícia. Restricted skew-morphisms on matrix algebras. Linear Algebra and its Applications, ISSN 0024-3795, 2016, vol. 490, str. 1-17.
2. DOLINAR, Gregor, GUTERMAN, Aleksandr Èmilevič, MAROVT, Janko. Monotone transformations on B(H) with respect to the left-star and the right-star partial order. Mathematical inequalities & applications, ISSN 1331-4343, 2014, vol. 17, no. 2, str. 573-589.
3. DOLINAR, Gregor, MOLNÁR, Lajos. Isometries of the space of distribution functions with respect to the Kolmogorov-Smirnov metric. J. math. anal. appl., 2008, letn. 348, št. 1, str. 494-498.
4. MAREŠ, Tomáš, DANIEL, Matej, PERUTKOVÁ, Šárka, PERNE, Andrej, DOLINAR, Gregor, IGLIČ, Aleš, RAPPOLT, Michael, KRALJ-IGLIČ, Veronika. Role of phospholipid asymmetry in the stability of inverted hexagonal mesoscopic phases. J. phys. chem., B Condens. mater. surf. interfaces biophys., 2008, letn. 112, št. 51, str. 16575-1658
5. ŠKERLJ, Tina, DOLINAR, Gregor, MRAMOR, Dušan. Estimation of asset accumulation of the proposed Slovenian mandatory-funded pension pillar. Acta oecon. (Bp.), 2001, letn. 51, št. 4, str. 513-539.
1. SULIĆ KENK, Vildana, MANDELJC, Rok, KOVAČIČ, Stanislav, KRISTAN, Matej, HAJDINJAK, Melita, PERŠ, Janez. Visual re-identification across large, distributed camera networks. Image and vision computing, ISSN 0262-8856, Feb. 2015, vol. 34, str. 11-26.
2. VODOPIVEC, Samo, HAJDINJAK, Melita, BEŠTER, Janez, KOS, Andrej. Vehicle interconnection metric and clustering protocol for improved connectivity in vehicular ad hoc networks. EURASIP Journal on wireless communications and networking, ISSN 1687-1499, 2014, 2014, 170, str. 1-14.
3. RUGELJ, Miha, SEDLAR, Urban, VOLK, Mojca, STERLE, Janez, HAJDINJAK, Melita, KOS, Andrej. Novel cross-layer QoE-aware radio resource allocation algorithms in multiuser OFDMA systems. IEEE transactions on communications, ISSN 0090-6778, Sep. 2014, vol. 62, no. 9, str. 3196-3208.
4. HAJDINJAK, Melita, BIERMAN, Gavin M. Extending relational algebra with similarities. Mathematical structures in computer science, ISSN 0960-1295, Aug. 2012, vol. 22, no. 4, str. 686-718.
5. HAJDINJAK, Melita, MIHELIČ, France. The PARADISE evaluation framework : issues and findings. Computational linguistics, ISSN 0891-2017, Jun. 2006, vol. 32, iss. 2, str. 263-272.

## Study materials

1. D. C. Montgomery, G. C. Runger: Applied statistics and probability for engineers, John Wiley & Sons, 6th Edition, 2013.
2. W. C. Navidi: Statistics for Engineers and Scientists, McGraw-Hill, 2007.
3. G. Turk: Verjetnostni račun in statistika, Ljubljana, 2011.
4. M. Hladnik: Verjetnost in statistika, Založba FE in FRI, Ljubljana, 2002.
5. R.S. Kenett, S. Zacks, D. Amberti: Modern Industrial Statistics: with Applications in R, MINITAB, and JMP, Wiley 2014.

## Bodi na tekočem

Univerza v Ljubljani, Fakulteta za elektrotehniko, Tržaška cesta 25, 1000 Ljubljana