Preface: the quarter I took this class, UCLA was affected by the COVID-19 pandemic, so the grades and class structure were probably skewed.

I've found that EE classes at UCLA tend to be extremely brutal, but this is one of the better ones. In no way is this class easy, it's just that while it's brutal, you actually learn the material extremely well, and Professor Dolecek has a good teaching style (at least for me personally). Honestly, for EC ENGR 131A, she's probably the best professor you're going to get. Sure you'll have hard exams but for the most part they're fair and she's a nice person who genuinely cares that students are learning (and helpful in office hours).
Originally, there were 8 scheduled problem sets, a final project [involving MATLAB], a midterm (only 1), and a final (due to COVID-19, the final exam was made optional however). Here is the original grading breakdown and then the modified one (if you opted out of the final):
15% - Homework
10% - MATLAB Project
30% - Midterm
45% - Final (optional for our quarter)
If you chose to opt out of the final exam, your grade was determined solely based off of the other factors. Lectures and discussions have a certain structure and pattern, which I found to be extremely consistent and conducive to student learning. For a 2 hour lecture, we had a 10 minute break at the 50 minute mark, and lectures always started off with an outline of today's new topics and a recap of last lecture. She follows all her theory with worked examples, and doesn't skip steps in the proofs, which is a plus. While she's slightly more on the theoretical side of teaching, for a course on probability and statistics, I have no qualms about that. Discussion sections were useful to me, as we reviewed the week's new material and practiced additional problems on reinforcing concepts. My TA (Lev Tauz), was really good at throwing some of his own questions to get us to think, and was very sociable.
One thing I must remark upon is the difficulty of this class. Leading up to the midterm, content and homework was very bearable, but afterwards they decided to ramp it up a notch. In particular, the last two homeworks took up a lot of time, and I felt they were a little unnecessarily long (and maybe slightly sadistic lmao). For the MATLAB project, make sure to start early (they assign it ~week 7 and it's due finals week), so that you can ask your questions early and get answers on how to do it, as opposed to starting it week 10 and spending the weekend before finals week trying to complete it. Midterm average was ~87%, which Professor Dolecek seemed pretty happy about, but don't be fooled: for previous years and most of the quarters she's taught this course, the exams are notoriously difficult and have much lower averages.
Overall, I definitely felt like I learned a lot throughout this course. You'll start off basic with set theory, transition to random variables, and then unify this with some of the higher principles of probability (e.g. Law of Large Numbers, Central Limit Theorem, etc.). While it's a difficult course, I promise you that if you stick with it, you'll feel extremely satisfied seeing your work come off, or being able to get the correct display for the MATLAB project, as it really makes you work for it but I guarantee you'll feel proud at the end of the day if you persevere. Definitely would take again for this course.

If you're a CS major (or basically any major not required to take 131A) don't take it imo. I would have taken Math170E or Stats100A in hindsight. The topics are interesting and presented well, but the TAs this year sucked at making exams. We had a pretty wide distribution for the midterm (70 median with 1 std dev getting you to a 90). Homeworks were pretty easy outside of some really dumb questions. Towards the end it became all calculus and no probability. Also, the final exam was terrible this winter. The TAs who wrote the exam changed one of the PDFs for a question worth 1/6 of the final exam about halfway through. There were too many questions also. A couple parts of some questions were just wacky algebra that we've never seen on discussion, homework, or in-class. It was a top 2 worst final exam experience and it's not #2.

Fair lecturer, fair exams. Dolecek is a very fair professor and clearly knowledgeable.

I can summarize this class in 2 words: Simple Calculus

This is a quite difficult class and goes at quite a fast pace. It is very important to not fall behind on material. Professor Dolecek is a great lecturer and explains things well. She also sets expectations quite well and the TAs make homework that is quite representative of the test difficulty, and if anything the homework is a bit more difficult. The class is topped with a project that is a bit of a grade booster, but make sure you start it on time. The professors notes are also quite good since she literally writes down everything she says, but sometimes it is a bit hard to read(fortunately there are anon questions on piazza!)

While not the easiest class out there, it was certainly doable. The grade breakdown for the quarter was as follows:
15% - Homework
20% - Exam 1
20% - Exam 2
20% - MATLAB Project
25% - Final
The professor was really clear in her explanations, but her handwriting could be hard to read at times. Lectures are done on iPad, recorded, and posted on Canvas. The homeworks were all doable, but also got harder as the class went on. These assignments were all representative of problems you'd see on the exams. Because of the quarter system, the class does go at an increasingly fast pace, and feels especially rushed by the end of the quarter.

I am a big fan of Professor Dolecek. She writes lots of clear notes in her lecture and I find it very easy to follow. I can always view her lecture notes on canvas and find exactly where she discusses a specific topic. Her midterms were both very fair and straightforward. The project was a decent amount of work but the TA and professor did a good job of walking us through it over the course of the last few weeks.

I'm not going to lie, the final hit me like a truck. It was much more difficult than I expected, and I did not do well. The other parts of the course were enough for me to hold the A but it was close. The exam made me upset at the time. I wish it was more like the midterms, but it's in the past. I still highly recommend taking this course with Dolecek as it is required. Out of the required classes for EE, this is one of the better ones. They are all rough.

Overall, I'm very happy with this class and its instructors (Lara Dolecek, Lev Tauz, Mitra Debarnab). I come from a CS background and have taken 1-2 machine learning classes (a few years ago) where they never really delved into the mathematical details of distributions, their origins and properties. This class helped fill that gap for me and I feel more confident in my understanding of the maths behind ML.

As for the class itself, it covers pretty much everything from the initial axioms that define probability up to common statistical measures such as covariance, squared error and correlation. I took this class remotely via the MSOL program and had a grade breakdown as follows:
-25% Homework (8 in total)
-25% Midterm (open book)
-25% Assignment (solo)
-25% Final (open book)

10 weeks is not a lot of time for this and it shows: the class moves at a fast pace, particularly towards the end. Even in the week of the final, a sizable number of new topics were introduced (fortunately, they did not feature in the exam). I personally did not do as well in the final exam, but got good grades otherwise, ending up with 88% overall.

Some tips for new students:
-The following concepts are useful to know: set theory, multivariable calculus (partial derivatives, double integrals, limits, convergence), convolution, Fourier transform, sums and sequences, complex numbers, gamma function and delta function. You don't need to know all of them, but most should be familiar.
-The textbook is your friend: it covers the content of the lectures at a higher level of detail and has useful examples when you're struggling with the homework.
-The discussions are helpful, as they will go over more advanced problems that the lectures do not address. Also, they are usually a bit more difficult than the exam, so if you take the time to solve and understand those you should be fine.
-The assignment is an easy way to boost your grades as the concepts are not particularly difficult. However, it does take quite a while to write up the MATLAB programs and report, so make sure to start it before the last week so you have some idea of how long it will take you.

Since I've already taken Math 170 sequence courses, I walked into this class without expecting to learn much. However, this was not the case. I thought I've already learned probability extremely well, but Professor Dolecek's teaching truly made my understanding clearer than ever. One of the highlights of this course was definitely the coding final project since we were able to simulate probabilistic scenarios with computation, and I had tons of fun with it. The professor was also pretty accommodating by creating an additional midterm to alleviate the pressure of depending on a single midterm. Overall, I would highly recommend taking this course with Professor Dolecek.

She doesn't upload any lectures or slides on CCLE, but she writes down everything on board, every concept from basic to advance, every proof even with the baby steps. She's really good at teaching and her lectures were amazing, were after taking her class I started to do a minor in math as well. Her class is based on weekly hws that involves matlab coding, a project at the end which she gives you at least 3-4 weeks to do it, and a midterm and final which is really similar to her leture examples not the hws.