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)