# Probability foundations for electrical engineers – EE5110

**Title :** probability foundations for electrical engineers

**Course No :** EE5110

**Credits :**

**Prerequisite :**

**Syllabus :**

- Probability Spaces, σ-algebras, events, probability measures
- Borel Sets and Lebesgue measure
- Conditioning, Bayes’ rule
- Independence
- Borel-Cantelli Lemmas
- Measurable functions, random variables
- Distribution functions, types of random variables
- Joint distributions, transformation of random variables
- Integration, expectation, covariance, correlation
- Conditional expectation and MMSE estimation
- Monotone convergence theorem, Dominated convergence theorem, Fatou’s lemma
- Transforms (Moment generating fufunction, characteristic function)
- Concentration Inequalities
- Jointly Gaussian random variables
- Convergence of random variables, various notions of convergence
- Central limit theorem
- The laws of large numbers (the weak and strong laws)

**Text Books :**

- Probability and Random Processes by Geoffrey R. Grimmett and David R. Stirzaker. Oxford University Press, 3rd edition, 2001.
- MIT OCW Notes (Course 6.436, hyperlink below)
- RELATED LINKS
- http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-436j-fundamentals-of-probability-fall-2008/lecture-notes/

**References :**

- Probability with Martigales by D. Williams, Cambridge University Press, 1991.
- A First Look at Rigorous Probability Theory by J. Rosenthal, World Scientific Publishing Co Pte Ltd; 2nd Revised edition, 2006.