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## Module: Foundations of Stochastic Processes (40256)

Note: This module is designed for students in the M.Sc. Elektrotechnik (ET) program under StuPO 2015 but it is also open to students of other study programs.

Students will acquire the fundamentals of Probability, Stochastic Processes and Statistics, which help form the basis of modern Electrical Engineering in the "systems" areas such as Automatic Controls, Communications, Computer Networks, and Signal Processing.

The accompanying tutorial is designed to complement the lecture. Its goal is to provide examples, and develop problem solving ability, related to the theoretical concepts covered in the lecture.

### Further Information

Quick Facts
Module Components:
One course consisting of two simultaneous components:
Probability and Stochastic Processes
-Lecture (4 LP)
-Tutorial (2 LP)
Duration of Module:
One semester
Type of examination:
Portfolio exam
Total LP:
6
Enrollment for exam:
QISPOS
Instructor:
Giuseppe Caire
Available to:
Elektrotechnik M.Sc.
Module Year:
2015/16
Material/Organization:
ISIS
LP = Leistungspunkte/Credits

### Module 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 Supporting Material

• Course notes and slides in electronic form are provided
• Literatur: Gubner, J. A. (2006). Probability and random processes for electrical and computer engineers . Cambridge University Press.

## LECTURE - Probability and Stochastic Processes

LV-Nr. 34331600 L 007
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Prof. G. Caire
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## TUTORIAL - Probability and Stochastic Processes

LV-Nr. 34331600 L 008
__________________
Prof. G. Caire
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