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)
  • 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.