19200601
Lecture
WiSe 19/20: Stochastics I
Timothy John Sullivan
Additional information / Pre-requisites
Zielgruppe:
Studierende ab dem 3. Semester
Voraussetzungen:
Grundkenntnisse aus Analysis und Linearer Algebra
Comments
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.
Suggested reading
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.
32 Class schedule
Additional appointments
Wed, 2020-02-12 12:00 - 15:00Klausur
Wed, 2020-02-12 15:00 - 16:00
Klausur
Regular appointments
Mon, 2019-10-14 08:00 - 10:00
Stochastik I (Serientermin 2)
Mon, 2019-10-21 08:00 - 10:00
Stochastik I (Serientermin 2)
Mon, 2019-10-28 08:00 - 10:00
Stochastik I (Serientermin 2)
Mon, 2019-11-04 08:00 - 10:00
Stochastik I (Serientermin 2)
Mon, 2019-11-11 08:00 - 10:00
Stochastik I (Serientermin 2)
Mon, 2019-11-18 08:00 - 10:00
Stochastik I (Serientermin 2)
Mon, 2019-11-25 08:00 - 10:00
Stochastik I (Serientermin 2)
Mon, 2019-12-02 08:00 - 10:00
Stochastik I (Serientermin 2)
Mon, 2019-12-09 08:00 - 10:00
Stochastik I (Serientermin 2)
Mon, 2019-12-16 08:00 - 10:00
Stochastik I (Serientermin 2)
Mon, 2020-01-06 08:00 - 10:00
Stochastik I (Serientermin 2)
Mon, 2020-01-13 08:00 - 10:00
Stochastik I (Serientermin 2)
Mon, 2020-01-20 08:00 - 10:00
Stochastik I (Serientermin 2)
Mon, 2020-01-27 08:00 - 10:00
Stochastik I (Serientermin 2)
Mon, 2020-02-03 08:00 - 10:00
Stochastik I (Serientermin 2)
Mon, 2020-02-10 08:00 - 10:00
Stochastik I (Serientermin 2)
Thu, 2019-10-17 08:00 - 10:00
Stochastik I (Serientermin 1)
Thu, 2019-10-24 08:00 - 10:00
Stochastik I (Serientermin 1)
Thu, 2019-10-31 08:00 - 10:00
Stochastik I (Serientermin 1)
Thu, 2019-11-07 08:00 - 10:00
Stochastik I (Serientermin 1)
Thu, 2019-11-14 08:00 - 10:00
Stochastik I (Serientermin 1)
Thu, 2019-11-21 08:00 - 10:00
Stochastik I (Serientermin 1)
Thu, 2019-11-28 08:00 - 10:00
Stochastik I (Serientermin 1)
Thu, 2019-12-05 08:00 - 10:00
Stochastik I (Serientermin 1)
Thu, 2019-12-12 08:00 - 10:00
Stochastik I (Serientermin 1)
Thu, 2019-12-19 08:00 - 10:00
Stochastik I (Serientermin 1)
Thu, 2020-01-09 08:00 - 10:00
Stochastik I (Serientermin 1)
Thu, 2020-01-16 08:00 - 10:00
Stochastik I (Serientermin 1)
Thu, 2020-01-23 08:00 - 10:00
Stochastik I (Serientermin 1)
Thu, 2020-01-30 08:00 - 10:00
Stochastik I (Serientermin 1)
Thu, 2020-02-06 08:00 - 10:00
Stochastik I (Serientermin 1)
Thu, 2020-02-13 08:00 - 10:00
Stochastik I (Serientermin 1)