EE 503: Probability for Electrical and Computer Engineers

University of Southern California, Fall 2025

Schedule

Week 1

Aug 26

Lecture 1 Logic and sets. Proof technique. Sigma-algebras. Probability axioms. Handout Daily Derivations Homework 1 Homework 1 - Handout Homework 1 Homework 1 - Book

Week 2

Sep 2

Lecture 2 Uncountability. Borel sigma-algebra. Independence. Total probability. Homework 2 Homework 2 - Handout Homework 2 Homework 2 - Argument Homework 2 Homework 2 - Book

Week 3

Sep 9

Lecture 3 Combinatorics. Limits of sequences and sets. Borel-Cantelli Lemma. Homework 3 Homework 3 - Handout Homework 3 Homework 3 - Book

Week 4

Sep 16

Lecture 4 Discrete probability. Poisson Law. Approximations. Handout BEG-CUP pdfs Homework 4 Homework 4 - Book

Week 5

Sep 23

Lecture 5 Random variables. Continuous densities. Bayes conjugate inference. Handout Normal table (z-table) Handout Chi-square table Homework 5 Homework 5 - Book

Week 6

Sep 30

Lecture 6 Expectations and higher moments of random variables. Homework 6 Homework 6 - Book

Week 7

Oct 7	Lecture 7 Covariance. Correlation. Uncertainty principles. Homework 7 Homework 7 - Book
Oct 9	No class: Fall Recess. Class rescheduled to Oct 7th at 18:00.

Week 8

Oct 14

Lecture 8 Stochastic convergence of random sequences. Laws of large numbers. Discussion Extra Session - Stochastic Convergence Homework 8 Homework 8 - Book

[Notes] Session Notes

Week 9

Oct 21

Lecture 9 Conditional expectations. S.I.T. technique. Maximum likelihood estimation. Handout t-table Homework 9 Homework 9 - Book

Week 10

Oct 28

Lecture 10 Transformed densities. Monte Carlo. Entropy and information. Mixtures. Homework 10 Homework 10 - Handout Homework 10 Homework 10 - Book

Week 11

Nov 4

Lecture 11 Central limit theorem. Confidence intervals. Numeric approximations. Homework 11 Homework 11 - Book

Week 12

Nov 11

Lecture 12 Financial engineering: probabilistic highlights. Martingales. Queues. Homework 12 Homework 12 - Handout

Week 13

Nov 18

Lecture 13 Markov processes and queues.

No class, Thanksgiving Holiday

Week 14

Dec 2

Lecture 14 Optimal estimation. Multiple regression. Least squares. Homework 13 Homework 13 - Handout Homework 13 Homework 13 - Book

Final Exam - Tuesday, December 16, 11:00 - 13:00