Probability Foundations
for Electrical Engineers

July-November 2017

I am releasing the PDF notes that are meant to accompany the NPTEL video course. I am grateful
to the scribes and TAs who worked for many hours typing up these class notes –
most of them are acknowledged by name in the PDF files.

I would like to inform the
reader that these notes have not been carefully edited, so you may find the
occasional bug, typo, inadequate citation, or less than perfect language in
some places. I would be grateful if such shortcomings are brought to my notice.

Module 0: Preliminaries

3. Cardinality and Countability

Module 1:
Probability Measures

5. Properties of Probability Measure

6. Discrete Probability Spaces

7. Borel Sets and Lebesgue Measure

8. The Infinite Coin Toss Model

9. Conditional Probability and Independence

Module 2:
Random Variables

11. (i) Random Variables (ii) Types of Random Variables

12. Multiple Random Variables and Independence

13. Conditional
Distributions, Joint Continuity

14. Introduction to Transformation of Random Variables

Module 3:
Integration and Expectation

17. Integration
and Expectation

19. The
Monotone Convergence Theorem

20. Expectation of Discrete RVs, Expectations over Different
Spaces

21. Expectation of Continuous RVs, Fatou’s Lemma, Dominated
Convergence Theorem

Module 4:
Transforms

24. Probability Generating Function

25. Moment Generating Function

27. Concentration Inequalities

Module 5:
Limit Theorems

28. Convergence of Random Variables