Statistical Reasoning 4.17.E.475

This subject develops the building blocks of probability theory that are necessary to understand statistical inference. The axioms of probability theory are reviewed, discrete and continuous random variables are introduced, and their properties are developed in the univariate and bivariate setting. In
particular, we discuss the most common probability distributions that arise in statistical applications. We then introduce methods for computing the distribution of sums of random variables, talk about convergence of random variables (in probability and in distribution) before stating two major theorems of probability theory: the law of large numbers, and the central limit theorem. The last part of this course introduces basic concepts in statistics, including properties of estimators (consistency, efficiency), maximum likelihood estimators and their asymptotic normal properties, and confidence intervals.

Supplementary literature

- Ross S., A first course in Probability, Pearson International Edition, 9th ed., 2013. ISBN-10: 1292024925. - Wonnacott T. H. and R. J. Wonnacott, Statistique: Economie - Gestion - Sciences - Médecine (avec exercises 'application), Paris, Economica, 4ème ed. 2000. - Howell D. C., Statistique en Sciences Humaines (M. Rogier, traduction française), Edition Deboeck, 2008. - Bouget D. et A. Viénot, Traitement de l'Information : Statistique et Probabilités, Edition Vuibert,1998.

Type of course

obligatory courses

Mode

(in Polish) Realizowany w sali

Learning outcomes

Learning Outcomes: A good understanding of the following topics:
• Essentials in probability theory
• Samples and sampling distributions
• Estimators
• Finite sample properties of estimators
• Asymptotic properties of estimators
• General methods to prepare estimators
• Interval estimation
• Hypothesis testing

Assessment criteria

Lecture: Exam
Exercises: Written-test on solving problems

Bibliography

Comte M. et J. Gaden, Statistiques et Probabilités pour les sciences économiques et sociales, Collection Mayor, PUF, 1ère édition, 2000.
- Wackerly D. D., Mendenhall W and R.L. Scheaffer, Mathematical Statistics with Applications, Duxbury Press, 7th ed., 2008.
- Mendenhall W, Beaver R. J. and B. M. Beaver, Introduction to Probability and Statistics, Duxbury Press, 14 ed. 2012.
- Ross S. M., Initiations aux Probabilités, traduction de la 4ème édition américaine, Collection : Enseignement des Mathématiques, Presses polytechniques et universitaires normandes.

Additional information

Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system:

Description of 4.17.E.475 in USOSweb