University of Hradec Králové, Faculty of Informatics and Management

Master Degree Exam Requirements

Subject:  Quantitative Methods

20013/14

 

  1. Measuring uncertainty. Probability, basic definitions and rules (addition rule for elementary events, conditional probability, multiplication rule, Bayes’ Theorem). Random variable, discrete and continuous probability distributions. Most common models of distribution (for example: alternative, binomial, Poisson, uniform, normal, exponential).
  2. Statistical Inference. Population and random sample, methods of sampling, sampling distribution, sampling error. Statistical point estimate, the quality of an estimate, confidence interval for mean and proportion.
  3. Law of large numbers, Central limit theorem and understanding the use.
  4. Principles of testing of statistical hypothesis, type I. and II. errors, hypothesis about population mean and proportion.
  5. Randomised design, One-way ANOVA. Explanation and the use of ANOVA, assumptions, hypothesis, post-hoc tests.
  6. One-way dependencies, correlation between quantitative statistical variables, coefficient of correlation, explanation of its properties, estimation, hypothesis.
  7. Regression function with one or more than one explanatory variables. An estimate of parameters of regression line, assumptions and the properties of the least squares regression estimate, quality of the model, use of the model for prediction, meaning of the regression coefficients, possible difficulties and avoiding them, significance tests in regression analysis.
  8. Time series analysis, modelling, components of time series, estimates for trend and seasonal components, quality of the model.
  9. Qualitative and categorial variable. Contingency table, hypothesis, tests of hypothesis, assumptions for their practial use.
  10. Linear Programming (LP) and Operations Research. Formulating the economic and mathematical models, preparing LP task, basic terminology, solving LP problems, the simplex method, solving distribution problems.
  11. Application of the graph theory and network analysis in economic modelling. Basic terminology of networks, the minimum spanning tree problem, the shortest path problem, project planning control with CPM and PERT
  12.  Stochastic and deterministic models. Stochastic processes. Applications of stochastic models. The inventory models. The applications of queuing theory.
  13. Renewal models: renewal table and solution with the use of regular Markov chain.
  14. Markov chains and their description, Chapman – Kolmogorov equation, first passage time, regular chains, absorption chains, long – run properties of Markov chains.
  15. Modelling the population processes, life table – inputs and output characteristics.
  16. Modelling and simulation. Random numbers and their use, congruent generators, transformation random numbers to random numbers from specific distributions. The assessment of the quality of random number generators (statistical properties). 

References:

Hebák P., Kahounová J.: Počet pravděpodobnosti v příkladech. Informatorium, Praha 2005.

Hindls R., Hronová S., Seger J.: Statistika pro ekonomy. Professional Publishing, Praha 2003 Jablonský J.: Operační výzkum. Kvantitativní modely  pro ekonomické rozhodování, Professional Publishing, Praha 2002

Skalská H.: Stochastické modelování. Gaudeamus, Hradec Králové, 2006

Skalská H.: Aplikovaná statistika. Sbírka elektronických textů, UHK 2003

Arltová M. a kol.: Sbírka příkladů ze statistiky (Statistika A). VŠE Praha, 1997

 

English References Equivalents:

Hillier F.S., Lieberman G.J.: Introduction to operations research. McGraw-Hill, 2004

Gentle E.J.: Random Number Generation and Monte Carlo Methods. Springer-Verlag, New York, 1998

Grinstead Ch., M., Snell J., L.: Introduction to Probability. Chance project publication, Render B., Stair R.: Quantitative Analysis for Management. Allyn and Bacon, Boston, 1994

McClave J.T., Benson P.G., Sincich T.:  Statistics for Business and Economics. Prentice Hall, Inc., 2003

Groebner D.F., Shannon P.W., Fry P.C., Smith K.D.: Business Statistics. A Decision Making Approach. Prentice Hall, 2005.