Moses - Foundations of Stochastic Processes

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Module / Version:
#40256 / #3

Validity:
Seit SS 2018

Default display language:
English

Module title:
Foundations of Stochastic Processes

Credits:
6

Responsible person:
Caire, Giuseppe

Grading:
benotet

Type of exam:
Mündliche Prüfung

Zugehörigkeit

Faculty:
Fakultät IV

Institute:
Institut für Telekommunikationssysteme

Area of expertise:
34331600 FG Theoretische Grundlagen der Kommunikationstechnik

Prüfungsausschuss:
No information

Kontakt

Office:
HFT 6

Contact person:
Caire, Giuseppe

E-mail address:
caire@tu-berlin.de

Website:

http://www.commit.tu-berlin.de/menue/lehre/parameter/en/

Learning Outcomes

Students acquire the fundamental background on Probability, Stochastic Processes and Statistics, which is at the basis of modern Electrical Engineering in the ``systems’’ areas such as Automatic Controls, Communications, Computer Networks and Signal Processing.

Content

- Axiomatic definition of probability: probability space - Equiprobable events, counting, and discrete probability - Random variables and cumulative distribution functions - Discrete random variables - Continuous random variables - Random vectors - Gaussian multivariate distributions and related distributions - Change of measure - Transform methods: probability generating function, characteristic function, moment generating function - Weak Law of large numbers, Central Limit Theorem, and large deviations - MMSE estimation and the orthogonality principle - Stochastic convergence - Markov Chains - Wide-sense stationary processes and spectral representation

Module Components

Pflichtgruppe:

All Courses are mandatory.

Course Name	Type	Number	Cycle	Language	SWS	VZ
Probability and Stochastic Processes	VL	34331600 L 007	WiSe	No information	3
Probability and Stochastic Processes	UE	34331600 L 008	WiSe	No information	1

Workload and Credit Points

Probability and Stochastic Processes (VL):

Workload description	Multiplier	Hours	Total
Attendance time	15.0	3.0h	45.0h
Preparation and postprocessing	15.0	3.0h	45.0h
Examination preparation, midterm	1.0	20.0h	20.0h
Examination preparation, final	1.0	25.0h	25.0h
			135.0h(~5 LP)

Probability and Stochastic Processes (UE):

Workload description	Multiplier	Hours	Total
Attendance time	15.0	1.0h	15.0h
Preparation and Homework	15.0	1.0h	15.0h
Examination preparation, midterm	1.0	5.0h	5.0h
Examination preparation, final	1.0	10.0h	10.0h
			45.0h(~2 LP)

The Workload of the module sums up to 180.0 Hours. Therefore the module contains 6 Credits.

Description of Teaching and Learning Methods

The module consists of conventional frontal teaching in class, developing theoretical and mathematical concepts, exercises developed in class, in order to develop problem-solving skills and reinforce comprehension of the theory, and homework exercises in order to develop independent and autonomous thinking skills in the students. Often, problems in probability and stochastic processes will be connected to aspects of electrical engineering, communications, signal processing and controls.

Requirements for participation and examination

Desirable prerequisites for participation in the courses:

Prerequisite for participation to courses are a mathematical background at the level of beginning MS students in Electrical Engineering (multivariate calculus, Fourier and Laplace Transforms, signals and systems, linear algebra and notions of matrix theory). The course is open to students enrolled in the Elektrotechnik MSc.

Mandatory requirements for the module test application:

1. Requirement

[CommIT] Passed written tests in the middle and at the end of the course

Module completion

Grading

graded

Type of exam

Oral exam

Language

English

Duration/Extent

30 minutes

Duration of the Module

The following number of semesters is estimated for taking and completing the module:
1 Semester.

This module may be commenced in the following semesters:
Wintersemester.

Maximum Number of Participants

This module is not limited to a number of students.

Registration Procedures

Course teaching and organization (not module examination enrollment at Examination office/Prüfungsamt) is supported by an ISIS course. Registration details are provided at the beginning of the module.

Recommended literature
Gubner, J. A. (2006). Probability and random processes for electrical and computer engineers. Cambridge University Press.

Assigned Degree Programs

Semester:

Zeige auch ausgelaufene Studiengänge und StuPOs

This module is used in the following Degree Programs (new System):

Studiengang / StuPO	StuPOs	Verwendungen	Erste Verwendung	Letzte Verwendung
Computer Engineering (M. Sc.)	1	39	SS 2018	SoSe 2024
Computer Science (Informatik) (M. Sc.)	1	46	SS 2018	SoSe 2024
Elektrotechnik (M. Sc.)	1	52	SS 2018	SoSe 2024
Information Systems Management (Wirtschaftsinformatik) (M. Sc.)	2	20	SS 2018	SoSe 2024
Technomathematik (B. Sc.)	1	13	SS 2018	SoSe 2024
Technomathematik (M. Sc.)	1	13	SS 2018	SoSe 2024
Wirtschaftsingenieurwesen (M. Sc.)	1	16	SS 2018	SoSe 2024

Students of other degrees can participate in this module without capacity testing.

Miscellaneous

No information

Foundations of Stochastic Processes