Winter 2026 Course Review: ECE 501¶

2026-05-05

Course Title: Probability and Random Processes

Rating: 3/5

Instructor (Sandeep Pradhan)¶

At this point in university, it no longer makes sense to comment on an instructor for the purpose of comparison, because there's no one else to compare to. Undergrads often say on Reddit, "avoid Prof. X, Prof. Y is much better", because they have a choice. Anyway, I'll keep on the tradition, so:

Chill guy, talks a lot, gives out chocolate on the three-hour exams, always welcomes us on office hours.

Course topics¶

First half is a review of undergrad probability (no statistics), but with more rigorous definitions such as the sigma algebra. We discuss discrete random variables, their expectation and variance, then introduce various laws, and generalize everything into continuous random variables. Then we study two variables (bivariate), then an arbitrary finite amount (random vectors), then infinite (random processes). Finally we study Markov chains and how select random processes can be described with them.

The underlying math is combinatorics (sometimes counting), a little bit of linear algebra (determinant of Jacobian), and LTI systems (Fourier transforms).

Homework¶

I quite often get stuck on homework. I'm the type of person who would rather leave it blank than ask AI, but it turns out to be disadvantageous to my grade if I left 3/4 of my homework blank, so I went to the office hour almost every week, usually to get help on homework. It worked. I still typically get lower than median, but I don't care.

Exams¶

The exams were atrociously long. There were three of them, and each was three hours long. The midterms were 18:00–21:00, and the final was 10:30–13:30. Each exam had 8 true/false questions, and you have to explain why it's true/false. Then what follows is three regular questions, arguably the same difficulty as true/false, so the exam can be seen as 11 questions, 8 of which come with a hint.

I finished midterm 1 slightly early, but on midterm 2 I was stuck on an inequality (there are three types of inequalities; I had two written on the front side of my cheatsheet and the last one on the back, and I forgot it exists until there was only 5 minutes left). I didn't exactly finish the final exam (left about three questions unfinished, like stuck on an integral), but still got a decent score. I forgot to put on my cheatsheet the formula for steady state distribution of a continuous time Markov chain, but I remembered how to approximate it with a discrete time Markov chain with infinetesimal time steps, then I took the limit to zero, which gave me the correct formula.

Math convention rant¶

In this course the sinc function is defined as sinc(x) = sin(πx) / πx, which is different from what I used in 216 (without the π). Also, Fourier transforms use 2πf instead of ω. Notably, this renders my previous Fourier transform tables invalid or at least inconvenient, so I had to piece together the version that works for this course.

Verdict¶

While not super relevant to my major, it's good to brush up on my math skills once in a while. Last time I properly did an integration was in my sophomore year, learning physics and LTI systems. Anyway, I finally know what a Markov chain is.