19200601 Lecture

# WiSe 19/20: Stochastics I

## Timothy John Sullivan

Zielgruppe:
Studierende ab dem 3. Semester
Voraussetzungen:
Grundkenntnisse aus Analysis und Linearer Algebra

Content

• Counting principles; combinatorial principles
• Models for processes influenced by chance: probability spaces and probability measures
• Conditional probability; independence; Bayes’ rule
• Random variables and their distributions; summary statistics of distributions: expected value and variance
• Discrete distributions: Laplace distribution; binomial distribution; geometric distributions
• Approximation of the binomial distribution by the normal distribution
• Approximation of the binomial distribution by the Poisson distribution
• Absolutely continuous distributions:  densities;  the uniform distribution; normal distributions;  exponential distribution
• Joint distributions of multiple random variables: discrete and with densities; independence; conditional distributions; sums of independent random variables and their distribution
• Statistics of multivariate distributions: expected value, covarince and correlation; conditional expectation; characteristic functiona
• Limit theorems: weak and strong laws of large numbers;  central limit theorem
• Data analysis and descriptive statistics: histograms; empirical diatribution; statistics of samples; examples of misleading descriptive statistics; linear regression
• Elementary terms and techniques of testing and estimation: Maximum likelihood principle; Confidence intervals; hypotheses tests; Type I and Type II errora

Literature

• E. Behrends: Elementare Stochastik, Springer, 2013
• H.-O. Georgii: Stochastik: Einführung in die Wahrscheinlichkeitstheorie und Statistik, De Gruyter, 2007
• U. Krengel: Einführung in die Wahrscheinlichkeitstheorie und Statistik, Vieweg, 2005
• D. Meintrup, S. Schäffler, Stochastik: Theorie und Anwendungen, Springer, 2005.
• Die meisten der unten aufgeführten Bücher gibt es online über die UB. Dazu gibt es in der Mathebibliothek einen umfangreichen Handapparat zur Stochastik.
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Literatur

• E. Behrends: Elementare Stochastik, Springer, 2013
• H.-O. Georgii: Stochastik: Einführung in die Wahrscheinlichkeitstheorie und Statistik, De Gruyter, 2007
• U. Krengel: Einführung in die Wahrscheinlichkeitstheorie und Statistik, Vieweg, 2005
• D. Meintrup, S. Schäffler, Stochastik: Theorie und Anwendungen, Springer, 2005.
• Die meisten der unten aufgeführten Bücher gibt es online über die UB. Dazu gibt es in der Mathebibliothek einen umfangreichen Handapparat zur Stochastik.
close

### 32 Class schedule

Wed, 2020-02-12 12:00 - 15:00
Klausur

Lecturers:
Prof. Dr. Timothy John Sullivan

Location:
HFB/A Hörsaal (Garystr. 35-37)

Wed, 2020-02-12 15:00 - 16:00
Klausur

Lecturers:
Prof. Dr. Timothy John Sullivan

Location:
HFB/A Hörsaal (Garystr. 35-37)

Regular appointments

Mon, 2019-10-14 08:00 - 10:00
Stochastik I (Serientermin 2)

Lecturers:
Prof. Dr. Timothy John Sullivan

Location:
A6/SR 031 Seminarraum (Arnimallee 6)

Mon, 2019-10-21 08:00 - 10:00
Stochastik I (Serientermin 2)

Lecturers:
Prof. Dr. Timothy John Sullivan

Location:
A6/SR 031 Seminarraum (Arnimallee 6)

Mon, 2019-10-28 08:00 - 10:00
Stochastik I (Serientermin 2)

Lecturers:
Prof. Dr. Timothy John Sullivan

Location:
A6/SR 031 Seminarraum (Arnimallee 6)

Mon, 2019-11-04 08:00 - 10:00
Stochastik I (Serientermin 2)

Lecturers:
Prof. Dr. Timothy John Sullivan

Location:
A6/SR 031 Seminarraum (Arnimallee 6)

Mon, 2019-11-11 08:00 - 10:00
Stochastik I (Serientermin 2)

Lecturers:
Prof. Dr. Timothy John Sullivan

Location:
A6/SR 031 Seminarraum (Arnimallee 6)

Mon, 2019-11-18 08:00 - 10:00
Stochastik I (Serientermin 2)

Lecturers:
Prof. Dr. Timothy John Sullivan

Location:
A6/SR 031 Seminarraum (Arnimallee 6)

Mon, 2019-11-25 08:00 - 10:00
Stochastik I (Serientermin 2)

Lecturers:
Prof. Dr. Timothy John Sullivan

Location:
A6/SR 031 Seminarraum (Arnimallee 6)

Mon, 2019-12-02 08:00 - 10:00
Stochastik I (Serientermin 2)

Lecturers:
Prof. Dr. Timothy John Sullivan

Location:
A6/SR 031 Seminarraum (Arnimallee 6)

Mon, 2019-12-09 08:00 - 10:00
Stochastik I (Serientermin 2)

Lecturers:
Prof. Dr. Timothy John Sullivan

Location:
A6/SR 031 Seminarraum (Arnimallee 6)

Mon, 2019-12-16 08:00 - 10:00
Stochastik I (Serientermin 2)

Lecturers:
Prof. Dr. Timothy John Sullivan

Location:
A6/SR 031 Seminarraum (Arnimallee 6)

Mon, 2020-01-06 08:00 - 10:00
Stochastik I (Serientermin 2)

Lecturers:
Prof. Dr. Timothy John Sullivan

Location:
A6/SR 031 Seminarraum (Arnimallee 6)

Mon, 2020-01-13 08:00 - 10:00
Stochastik I (Serientermin 2)

Lecturers:
Prof. Dr. Timothy John Sullivan

Location:
A6/SR 031 Seminarraum (Arnimallee 6)

Mon, 2020-01-20 08:00 - 10:00
Stochastik I (Serientermin 2)

Lecturers:
Prof. Dr. Timothy John Sullivan

Location:
A6/SR 031 Seminarraum (Arnimallee 6)

Mon, 2020-01-27 08:00 - 10:00
Stochastik I (Serientermin 2)

Lecturers:
Prof. Dr. Timothy John Sullivan

Location:
A6/SR 031 Seminarraum (Arnimallee 6)

Mon, 2020-02-03 08:00 - 10:00
Stochastik I (Serientermin 2)

Lecturers:
Prof. Dr. Timothy John Sullivan

Location:
A6/SR 031 Seminarraum (Arnimallee 6)

Mon, 2020-02-10 08:00 - 10:00
Stochastik I (Serientermin 2)

Lecturers:
Prof. Dr. Timothy John Sullivan

Location:
A6/SR 031 Seminarraum (Arnimallee 6)

Thu, 2019-10-17 08:00 - 10:00
Stochastik I (Serientermin 1)

Lecturers:
Prof. Dr. Timothy John Sullivan

Location:
A6/SR 031 Seminarraum (Arnimallee 6)

Thu, 2019-10-24 08:00 - 10:00
Stochastik I (Serientermin 1)

Lecturers:
Prof. Dr. Timothy John Sullivan

Location:
A6/SR 031 Seminarraum (Arnimallee 6)

Thu, 2019-10-31 08:00 - 10:00
Stochastik I (Serientermin 1)

Lecturers:
Prof. Dr. Timothy John Sullivan

Location:
A6/SR 031 Seminarraum (Arnimallee 6)

Thu, 2019-11-07 08:00 - 10:00
Stochastik I (Serientermin 1)

Lecturers:
Prof. Dr. Timothy John Sullivan

Location:
A6/SR 031 Seminarraum (Arnimallee 6)

Thu, 2019-11-14 08:00 - 10:00
Stochastik I (Serientermin 1)

Lecturers:
Prof. Dr. Timothy John Sullivan

Location:
A6/SR 031 Seminarraum (Arnimallee 6)

Thu, 2019-11-21 08:00 - 10:00
Stochastik I (Serientermin 1)

Lecturers:
Prof. Dr. Timothy John Sullivan

Location:
A6/SR 031 Seminarraum (Arnimallee 6)

Thu, 2019-11-28 08:00 - 10:00
Stochastik I (Serientermin 1)

Lecturers:
Prof. Dr. Timothy John Sullivan

Location:
A6/SR 031 Seminarraum (Arnimallee 6)

Thu, 2019-12-05 08:00 - 10:00
Stochastik I (Serientermin 1)

Lecturers:
Prof. Dr. Timothy John Sullivan

Location:
A6/SR 031 Seminarraum (Arnimallee 6)

Thu, 2019-12-12 08:00 - 10:00
Stochastik I (Serientermin 1)

Lecturers:
Prof. Dr. Timothy John Sullivan

Location:
A6/SR 031 Seminarraum (Arnimallee 6)

Thu, 2019-12-19 08:00 - 10:00
Stochastik I (Serientermin 1)

Lecturers:
Prof. Dr. Timothy John Sullivan

Location:
A6/SR 031 Seminarraum (Arnimallee 6)

Thu, 2020-01-09 08:00 - 10:00
Stochastik I (Serientermin 1)

Lecturers:
Prof. Dr. Timothy John Sullivan

Location:
A6/SR 031 Seminarraum (Arnimallee 6)

Thu, 2020-01-16 08:00 - 10:00
Stochastik I (Serientermin 1)

Lecturers:
Prof. Dr. Timothy John Sullivan

Location:
A6/SR 031 Seminarraum (Arnimallee 6)

Thu, 2020-01-23 08:00 - 10:00
Stochastik I (Serientermin 1)

Lecturers:
Prof. Dr. Timothy John Sullivan

Location:
A6/SR 031 Seminarraum (Arnimallee 6)

Thu, 2020-01-30 08:00 - 10:00
Stochastik I (Serientermin 1)

Lecturers:
Prof. Dr. Timothy John Sullivan

Location:
A6/SR 031 Seminarraum (Arnimallee 6)

Thu, 2020-02-06 08:00 - 10:00
Stochastik I (Serientermin 1)

Lecturers:
Prof. Dr. Timothy John Sullivan

Location:
A6/SR 031 Seminarraum (Arnimallee 6)

Thu, 2020-02-13 08:00 - 10:00
Stochastik I (Serientermin 1)

Lecturers:
Prof. Dr. Timothy John Sullivan

Location:
A6/SR 031 Seminarraum (Arnimallee 6)