Discrete Probability Theory
Module IN0018
This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.
Module version of SS 2015 (current)
There are historic module descriptions of this module. A module description is valid until replaced by a newer one.
Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.
available module versions  

SS 2015  WS 2011/2 
Basic Information
IN0018 is a semester module in German language at Bachelor’s level which is offered in summer semester.
This Module is included in the following catalogues within the study programs in physics.
 Further Modules from Other Disciplines
Total workload  Contact hours  Credits (ECTS) 

180 h  75 h  6 CP 
Content, Learning Outcome and Preconditions
Content
++ probability spaces, events, principle of inclusion/exclusion, Boolean inequality, conditional probability, multiplication theorem, total probability theorem, Bayesian theorem, independence
++ random variables, expected value, variance, linearity of expected value, conditional random variables and their expected value, variance, moments and central moments, several random variables and their common density & distribution, independence from random variables, moments of composite random variables, indicator variables
++ discrete distributions: Bernoulli distribution, binomial distribution, geometric distribution, coupon collector problem, Poisson distribution, relationships among distributions
++ methods for estimating probabilities, inequalities of Markov and Chebyshev, Chernoff barriers
++ Law of large numbers
++ Probabilitygenerating functions and their application to distributions, momentgenerating functions with various applications
continuous probability spaces
++ continuous random variables, Kolmogorov axioms, sigma algebras, Lebesgue integrals, computing with continuous random variables, simulation of random variables
++ continuous distributions: Equal distribution, normal distribution and linear transformation, exponential distribution and waiting processes, relationship with discrete distributions
++ several continuous random variables, boundary distributions and independence, sums of random variables
++ Moment generating functions for continuous random variables
++ Central limit theorem
Inductive Statistics
++ estimation variables, maximum likelihood principle, confidence intervals, hypothesis testing, statistical test development and application
Stochastic processes
++ processes with discrete time, Markov chains, transition probabilities, arrival probabilities, transition times, return times, fundamental theorem for ergodic Markov chains
Learning Outcome
 Participants are familiar with important concepts of discrete and continuous probability spaces and stochastic processes and can in large part deduce them themselves
 master calculation rules for the determination and estimation of probabilities, expected values and variances,
 are able to map real problems to abstract probability spaces and
 can easily apply simple statistical tests.
Preconditions
Courses, Learning and Teaching Methods and Literature
Courses and Schedule
Type  SWS  Title  Lecturer(s)  Dates  Links 

VO  3  Discrete Probability Theory (IN0018)  Albers, S. 
Fri, 12:00–15:00, MW 2001 and singular or moved dates 

UE  2  Discrete Probability Theory, Exercise Session (IN0018); We, Thu, Fr  Albers, S. Schubert, S.  dates in groups  
UE  2  Discrete Probability Theory, Exercise Session (IN0018); Mo, Tue  Albers, S. Schubert, S.  dates in groups 
Learning and Teaching Methods
Media
Literature
 Nobert Henze: Stochastik für Einsteiger, Vieweg, 2004
 R. Mathar, D. Pfeifer: Stochastik für Informatiker, B.G. Teubner Stuttgart, 1990
 M. Greiner, G. Tinhofer: Stochastik für Studienanfänger der Informatik, Carl Hanser Verlag, 1996
 H. Gordon: Discrete Probability, SpringerVerlag, 1997
 R. Motwani, P. Raghavan: Randomized Algorithms, Cambridge University Press, 1995
 L. Fahrmeir, R. Künstler, I. Pigeot, G. Tutz: Statistik  Der Weg zur Datenanalyse, SpringerVerlag, 1997
Module Exam
Description of exams and course work
Exam Repetition
The exam may be repeated at the end of the semester.
Current exam dates
Currently TUMonline lists the following exam dates. In addition to the general information above please refer to the current information given during the course.
Title  

Time  Location  Info  Registration 
Discrete Probability Theory  
Wed, 20220810, 13:45 till 15:45  1450 003 004 102 00.02.001 1550 2502 21010 0001 2001 1801 Hörsaal 
till 20220630 (cancelation of registration till 20220803) 