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t.BA.XXM5.STS.19HS (Stochastics and Statistics)

Module: Stochastics and Statistics

This information was generated on: 27 September 2021

No.

t.BA.XXM5.STS.19HS

Title

Stochastics and Statistics

Organised by

T IAMP

Credits

4

Description

Version: 2.0 start 01 August 2021

Short description

Introduction to the theory of probability and statistics.

Module coordinator

Tom Weinmann (weto)

Learning objectives (competencies)

Objectives

Competences

Taxonomy levels

Students are familiar with the basic terms and concepts of the theory of probability and are able to create and analyze probabilistic models.

F,M

3,4,5,6

Students are able to use probabilistic methods for the analytical as well as numerical calculation of probabilities.

F,M

3,6

Students understand the concept of random variables and the properties of the probability density function and the distribution function.

F,M

3,4

Students are familiar with the most important distributions and understand the concept of the joint distribution, the conditional distribution as well as the concept of covariance and correlation of random variables.

F,M

3,5

Students understand the laws of large numbers and the central limit theorem and grasp their impact on statistical applications.

F,M

3,5

Students are familiar with the most important methods for estimating parameters and testing hypotheses and are capable to apply these methods.

F,M

3,4

Module contents

Basic terms:
- probability spaces
- independence of events
- combinatorics and probability
- probability of unions

Conditional probability:
- multiplication rule
- rule of total probability
- Bayes' theorem

Discrete random variables:
- distribution of a random variable
- expected value of a random variable
- variance and standard deviation of a random variable
- some discrete distributions (binomial, multinomial, poisson, ...)

General random variables:
- expected value and variance of absolutely continuous random variables
- Some continuous distributions (uniform distribution, exponential distribution, normal distribution, ...)
- transformations of random variables
- joint distribution, marginal distribution and conditional distribution
- sums of independent random variables
- covariance, variance and correlation

Limit theorems:
- laws of large numbers
- central limit theorem

Statistical concepts:
- point estimates (method of moments, maximum likelihood method)
- interval estimates (expected value of a normal distribution with known / unknown variance, expected value of any distribution for large samples, ...)
- testing hypotheses (binary hypotheses, parametrized hypotheses, hypotheses about the distribution function, ...)

Teaching materials

Depending on the lecturer: script, slides, exercise series

The module description is part of the legal basis in addition to the general academic regulations. It is binding. During the first week of the semester a written and communicated supplement can specify the module description in more detail.