Probability theory 1

Mathematics BSc
Course description
2013.

Eötvös Loránd University
Faculty of Science
Institute of Mathematics

Borromean Rings

All courses
Core courses
- Algebra, number theory
- Analysis
- Geometry
  - Geometry 1
- Discrete mathematics
  - Discrete mathematics 1
  - Discrete mathematics 2
- Elementary mathematics
  - Elementary mathematics 1
- Informatics
  - Prog. fundamentals
Pure mathematics
- Algebra, number theory
- Analysis
  - Analysis 3
  - Analysis 4
  - Applied analysis
    - Numerical analysis
    - Appl. anal. comp.
  - Differential equations
    - Differential equations
    - Partial diff. equations
  - Topology
    - Introduction
    - Algebraic topology
  - Complex analysis
  - Functional analysis
  - Function series
- Geometry
- Operations research
  - Operations research 1
  - Operations research 2
- Probability theory
- Informatics
- Computer science
- Foundations of math.
  - Set theory
  - Mathematical logic
Applied mathematics
- Analysis
  - Analysis 3
  - Analysis 4
  - Analysis 5
  - Applied analysis
  - Differential equations
    - Differential equations
    - Partial diff. equations
  - Complex analysis
  - Functional analysis
- Geometry
- Operations research
  - Operations research 1
  - Operations research 2
- Probability theory
- Applied modules
- Informatics
- Algorithms
- Algebra
- Elementary mathematics
  - Elementary mathematics 2
  - Elementary mathematics 3
- Foundations of math.
BSc: general information
Studies

Probability theory 1

Hours lect+pc	Credits lect+pc	Assessment	Specialization	Course code lect/pc	Semester	Status
2 + 2	2 + 3	exam + term grade	applied math.	mm1c1vs3a mm1c2vs3a	3	compulsory

Course coordinator

András Zempléni
Department of Probability Theory and Statistics
Institute of Mathematics

Strong	Weak	Prerequisites
Practice class
		Strong: Discrete mathematics1L (mm1c1vm1)
		Strong: Analysis2L (mm1c1an2) or Foundations of analysisL (mm1c1ap2)
Lecture
Lecture		Weak: practice class

Remarks

Syllabus designed by:

András Zempléni, Department of Probability Theory and Statistics, Institute of Mathematics.

Literature

Recommended:

Sheldon Ross: A First Course in Probability. 9^th Edition, Pearson Educational Ltd., 2014.

Syllabus

Probability, elementary properties. Axioms of probability.
Conditional probability. Bayes' theorem. Independence. Expectation, standard deviation, conditional expectation.
Random walk, probability of ruin.
Random variables (vectors). Distribution- and density function. Most important discrete and continuous distributions. Independent random variables.
Generating function, convolution.
Famous inequalities (Markov, Chebyshev). Covariance and correlation.
The weak and strong law of large numbers. Central limit theorem (without proof).