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Problems of Probability and Statistics - NMSA160

Title:	Pravděpodobnostní a statistické problémy
Guaranteed by:	Department of Probability and Mathematical Statistics (32-KPMS)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2012 to 2015
Semester:	summer
E-Credits:	5
Hours per week, examination:	summer s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech
Teaching methods:	full-time

Guarantor:	doc. RNDr. Zbyněk Pawlas, Ph.D.
Teacher(s):	doc. RNDr. Zbyněk Pawlas, Ph.D. RNDr. Michaela Prokešová, Ph.D.
Class:	M Bc. FM M Bc. FM > Doporučené volitelné M Bc. FM > 1. ročník M Bc. MMIB M Bc. MMIB > Doporučené volitelné M Bc. MMIB > 1. ročník M Bc. OM M Bc. OM > Zaměření STOCH M Bc. OM > Doporučené volitelné M Bc. OM > 1. ročník
Classification:	Mathematics > Probability and Statistics
Incompatibility :	NSTP003, NSTP064

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Annotation -

Introduction to discrete probability and solutions of interesting problems by simple probabilistic and statistical methods. An elective course for 1st year students of General and Financial Mathematics.

Last update: G_M (16.05.2012)

Aim of the course -

To acquaint students with the basic methods that are used to describe and study processes influenced by chance.

Last update: Pawlas Zbyněk, doc. RNDr., Ph.D. (05.09.2012)

Literature - Czech

J. Anděl (2007): Matematika náhody, 3. vydání, Matfyzpress, Praha.

J. Bewersdorff (2005): Luck, Logic, and White Lies: The Mathematics of Games, A K Peters, Wellesley.

H. Tijms (2004): Understanding Probability: Chance Rules in Everyday Life, Cambridge University Press, Cambridge.

K. Zvára, J. Štěpán (2006): Pravděpodobnost a matematická statistika, 4. vydání, Matfyzpress, Praha.

Last update: T_KPMS (06.05.2013)

Teaching methods -

Lecture + exercises.

Last update: T_KPMS (15.05.2012)

Syllabus -

1. Random event with finitely many outcomes, classical probability.

2. Combinatorial probability.

3. Geometric probability, Bertrand's paradox.

4. Independence of random events, conditional probabilities, Bayes' theorem, medical diagnosis, Simpson's paradox.

5. Discrete random variable, its distribution, expectation and variance.

6. Problems of calculating the expectation.

7. Random walk, gambler's ruin.

8. Normal distribution, limit theorems.

9. Records, their expected number, waiting time for the next record.

10. Optimization problems, flight overbooking problem, partner selection problem.

Last update: Pawlas Zbyněk, doc. RNDr., Ph.D. (15.09.2013)