Combinatorics and Probability

Lecturer:

Tomáš Hobza (gar.)

Tutor:

Tomáš Hobza (gar.)

Supervisor:

Department of Mathematics

Synopsis:

The course is devoted to combinatorial rules, definition of the probability, explication of random variable and its characteristics. It explains term of distribution function and examples of discrete and continuous random variables are mentioned. Emphasis is placed on using of these terms and rules.

Requirements:

Basic course of Calculus

(in the exten of thecourses 01MAT1, 01MAT2 held at the FNSPE CTU in Prague).

Syllabus of lectures:

1.Combinatorial rules, variation, combination, permutation (with repetition and without repetition), properties of binomial coefficient, the binomial theorem

2. The classical definition of probability, the geometric probability definition, the mathematical model of probability (events, calculus of events, axioms of probability, dependence and independence of events)

3. Random variables (probability distribution function, discrete and continuous random variables and examples of these variables)

4. Expected value, variance, moments of random variables, the law of large numbers, the central limit theorem

Syllabus of tutorials:

Study Objective:

Knowledge:

Basic combinatorial rules, fundamentals of probability theory.

Skills:

Application of theoretical knowledge to solution of concrete problems. Ability of calculation of probability (conditional and unconditional), computation of moments of random variables and application of the central limit theorem.

Study materials:

Keyreferences:

[1] D.C. Montgomery, G.C. Runger: Applied statistics and probability for engineers, Wiley, 2003

Recommended references:

[2] H. G. Tucker: An introduction to probability and mathematical statistics, Academic Press, 1963

Note:

Time-table for winter semester 2011/2012:

Time-table is not available yet

Time-table for summer semester 2011/2012:

Time-table is not available yet

The course is a part of the following study plans: