# W4150 Introduction to Probability and statistics

- Departments: Industrial Engineering and Operations Research
- Professors: Mark Brown, Guillermo Gallego, Sandeep Juneja, and Daniel Rabinowitz

He can't teach, he can't be bothered posting accurate, up-to-date homework assignments on time. His practice exams do resemble the actual exams, and are extremely important to doing well in the class, but good luck understanding his badly written (often massively incorrect) solutions until the review session, which he likes to schedule a few days prior to his exams.

Other reviewers have written that doing the homework is important to doing well in the course. I disagree. Just study the solutions to practice exams in the 24-72 hours that he gives you to do so. Good luck if you have back to back exams in that time window.

Overall, he's a typically incompetent stats instructor, and like most of his ilk, will continue to bring pain, misery, and hatred of stats to students the world over.

#### Workload:

A lot if you do what he asks. Very little indeed if you're wise enough to only prepare for his exams, which cover 1/100 of the material.

There are few professors at Columbia which every student I have talked to dislikes, at Mark Brown manages to be one of them. This class is not actually very difficult, nor does it move fast, so it is probably best for you to learn from the textbook (which isn't amazing but not horrible) rather than go to class. The best option is to read the textbook and then supplement it with class, but if you do go to class (like I did), you should, at minimum, skim the textbook, or you will be horribly lost. Professor Brown gives little context for what he is doing. He does not tell you what he is trying to prove (which makes following proofs difficult since you have no idea where he is headed) and he rarely explains the conceptual nuance of what is going on. He also spends almost all his time in class proving things whereas, apart from the Extra Credit on the final exam, every exam and homework question is an application question, which means understanding the proofs is of little to no help in tackling the homeworks or exams.

Apart from his inability to explain concepts, Mark Brown rarely pays attention to his students. He is 50/50 with being able to understand student questions, he rarely responds to email (and if he does, he is rude), and he doesn't return homework in a timely manner (we got a homework due in October returned on the last day of class).

Overall, the material covered in this class is not difficult, and there is not a lot of it either. Even though this was, by far, my lowest workload class, it was the one I complained about the most because going to class with Professor Brown is a truly painful experience. If you learn the material on your own, and make sure you understand the concepts behind what's going on, this class won't be a high workload, nor will it be hugely difficult. Professor Brown provides a fairly generous curve, but given that most people take this class because it is a pre-requisite for other things, I would recommend taking this with another professor so that you truly understand the material.

For sake of disclosure, I got an A+ in his class, so I think it is fair to say that my unfavorable review of Professor Brown is not due to my grade. He is the worst professor I have encountered at Columbia, and from what I hear, that Statistics department is fairly notorious for having bad professors.

#### Workload:

4 Homework Assignments. Yes, only 4. They aren't very long. (25%)

Midterm Exam. Very Easy (25%)

Final Exam. Moderate to Easy. Harder than Midterm. (50%)

Professor Gallego looks to be a very nice person and a decent instructor. Everything he teaches is really at a very basic level and so is his homework. His exams were quite straightforward and did not require a high-level mathematical or calculus ability but a very deep understanding on Probability and Statistics. At a glance his exams look very easy but they are not. His exams are very similar with previous years exams but not with the two last years which he gave in class. If you can gain access to a series of his previous 5 years exams (final and midterm), those are the only things that are relevant with his exams.

The textbook "Introduction to Probability and Statistics" by Stephen Ross is not quite relevant with his exams. Do not study from the homework taken from that book because they definitely will not come out on the midterm/final. Except some additional problems from him (usually in a LaTeX pdf).

Materials that are relevant with his exams:

1. Last 5 years exams (if you somehow can gain access to those).

2. Formula derivations in his class notes. The very part that is worth studying is when he discuss about tables and derivations in his notes - others are not quite relevant. So, when you see some tables and some derivation, you should really understand those or try to derive them manually.

3. Sample exams he gave in class. Never expect that they will come out 100% but his exam will be quite similar.

4. "A First Course to Probability" book by Stephen Ross. This book definitely helps you study for the probability part. Try to master especially Joint Continuous Density from this book, Central Limit Theorem, Bayesian Theorem from this book. It will help you get an A. Try to score as high as possible on midterm although he says he will drop the midterm if you score higher on final but, no one scores higher on final. Try to understand on Gaussian Distribution and Uniform Distribution.

5. Prof Stephen Kou's Statistics lecture notes on MLE and Method of Moment. In his notes, he will give a table on MLE and Method of Moment estimates on exponential distribution but on the exam he asked to derive MLE and Method of Moment parameter estimates on double exponential distribution. And also try to solve Prof Kou's problems on Bayesian inference (prior-posterior), that will come out on the final.

6. Try to understand really deeply about the concepts of confidence level, significance level, and area of reaction under different distributions (not only Gaussian, student-t, or Chi-Square) because he will ask different distributions and will intertwine those terms (confidence level and significance level) which will make you confused if you do not understand those concepts in depth.

7. Goodness of Fit chapter of "Introduction to Probability and Statistics" by Stephen Ross. You should be able to use Chi-Square Test to test the independence between two variables.

8. Multiple Regression Part of Econometric Books. His notations on Regression part is very different from "Introduction to Probability and Statistics" book. One book that is quite similar in notation is Gujarati's econometrics. Try to solve some Multiple Regression problems in matrix form from that book.

He will allow one page 2-sided cheat sheet on midterm, two pages 2-sided cheat sheet on the final. Use your time from the beginning of the semester to make the cheat sheet.

#### Workload:

It is like a 6-credit course but will give you a very strong fundamental to take Stochastic course in the following semester.

I took this course over a year ago and I'm still pissed about it. See, I actually took a course in Probability and Statistics not because I had to in order to fulfill a requirement, but because I knew that I'd eventually be doing things where stats would come in handy. Sadly I wasted time and GPA on this utterly crap class.

First off, he likes playing with technology and he uses his tablet PC to project his drawings. The problem is, (and you know this if you've ever used a tablet PC), drawing with a tablet PC is like making notes on index cards with a 3/4" crayon. The lines are fat, the information density is low and ultimately you're just going to make a gigantic mess that is marginally useful.

Second, he uses a terrible book and moreover does not technically use the book. He covers theoretical stuff in class, sort of, with his giant crayon machine and then assigns plug and chug problems from the book. Are you familiar with convolution? If you are, you know that a serious course spends a minimum of a half session up to maybe two sessions discussing it, but not Gallego, you get 30 seconds and some crayon scratchings. Want to know more about it? You won't find anything in the book!

But whatever, I could complain all I want about his style. At the end of the day, the real issue is that the class is useless. I didn't learn a damned thing and have recently taught myself many of the topics covered by just Googling for books used by professors that give a shit and pulling down PDFs of those texts.

In any event, if you have to take this class because of a requirement, be prepared for a gigantic waste of time. If you don't, please take my advice and look elsewhere for a decent treatment of the material.

Honestly, this is the only Columbia class I have taken that I would consider demanding a refund for.

#### Workload:

Weekly plug and chug book problems. Long cram sessions before the exams (the practice tests he distributes right before the exams are the only cue as to what is actually expected). Many hours of general pissed-offed-ness about the ridiculousness of the situation.

If there is one thing you should take from this review it's this: AVOID THIS PROF AT ALL COSTS.

Unless you have been doing probstat for a while or you enjoy suffering, this class is terrible.

The Good:

I'm done with it.

The Bad:

His lectures involve him talking to his tablet while most of the class can't understand what he's trying to say. His handwriting is illegible. He scribbles down three lines per page and then moves on while most of us are trying desperately to copy down the notes. Taking notes AND paying attention.. good luck with that. That wouldn't be so bad if you could just read the textbook but he makes it a point to tell the class that the textbook he uses is not on the level of the class. Except he gives most of his homework from it. On the rare occasion he does give homework that reflects the level he will test you on, most people struggle with it and never truly get it. By the time you have anything to study from (the practice tests) you're pretty much screwed anyway.

He also says at the beginning of class he will curve to a B/B+.. That's crap because I hit exactly mean on both the midterm and final and received a B-. I may be bitter and this review is definitely biased because of it but this truly was an awful class.

#### Workload:

10 problem sets, most problems from the book.

The midterm wasn't terrible but as most people had never seen questions like that before it was tricky. The final was impossible. The only way to get through it was have a great cheat-sheet and copy down EVERY practice problem.

Everything that's been said about Gallego by previous reviewers has been pretty much spot on. Basically, you'll fall under the impression that you are learning something from his lectures and the hw, but when it comes to exam time, he throws all sorts of theoretical questions at you, and you're pretty much screwed. This dilemma is like being taught how to hammer a nail, then being expected to build a complete house. Don't get me wrong, Gallego is a friendly guy, but his exams will make you think otherwise.

To succeed in this class, you need to know the theoretical stuff cold. Focus on his handouts and review his practice exams until you know the material inside out. Use your cheat sheet wisely: copy down the theoretical practice exam questions and their solutions (this saved my butt on the final.)

This class would have been bearable if we were given homework that actually reflected the content on exams. For an "intro" 4000 level class, it felt unnecessarily complicated at times. (Compared to Polvani's Complex Variables E4204 class which I took concurrently, it was much harder.) On a positive note, after taking this class, you probably still learned more than the people taking Stat W1211.

#### Workload:

HW: 10 easy problem sets (although the last one had two tricky proofs on it-an aberration from the usual number crunching problems) [15%]

Midterm- mean was 56 (keep in mind there were LOTS of grad students in this class): in retrospect, not too bad, but tricky theoretical stuff is tested [40%]

Final- insane: without that cheat sheet, there's no way I would've passed. [45%ï¼Œwill become 85% if you do better on final than midterm]

This class is totally schizophrenic. On the one hand are the friendly lectures and problem sets. On the other hand are the TERRORIZING EXAMS. Twice a week, you sit down with Guillermo, and he explains, quite clearly, how everything works, and how to apply all of the methods. Once a week, you sit down with your textbook, and learn how to use the methods yourself. Friendly! Straightforward! Yay1

You're tempted into statistical complacency. It becomes an easy routine. YOU ARE BEING FOOLED! You think you understand the material? YOU DON'T KNOW ANYTHING! Exams don't test a skillset that you would develop listening to lectures, or reading the book, or completing the problemsets. They tests a fundamental understanding of the statistical methods.

The fundamental disconnect between the domain of knowledge tested by the homeworks and exams makes it so that by the time you have the opportunity to study for the exams, to a large extent, it's already too late.

#### Workload:

Easy weekly homeworks straight out of the book. 2 very difficult exams.

I took this class with Professor Juneja over the summer, and I must say he's the best professor I've had in years. He's normally a professor in India but does summer stints each year at Columbia. He's very intelligent, kind, laid back, and receptive to student questions, however dumb they may be. He stretched my personal limit for mathematical density with nitty gritty proofs, but I was better for it. My only pet peeve with his lecture style was his tendency to erase stuff on the board before people have had a chance to copy it down.

Regarding the material, don't ignore the calc prereq. The way the material is presented, you don't actually see calc until the second term, but all of the sudden you're asked to do integration by parts and other BC calc type problems. (I felt sorry for the poor soul in the front row on the first day of our work with integrals who raised her hand, pointed to the integral symbol, and said "What's THAT?!") Prof Juneja really knows how to get your interest though by tying things into real world problems. He levels with you that the stat part of the class toward the end is much more boring, and he's right. Still, everyone with a science background should have some of this stuff.

#### Workload:

We had 5 problem sets. In the beginning they weren't to bad, but they got more difficult later. Also, he fell a little behind and had to squish a lot of material in at the end. The last problem set had as many problems as the previous 3 combined, and they were only given to us about a week before the exam, so it required some serious cramming.

Unless your good at tricky math problems that require you to see shortcuts, the tests are very hard. The averages for the midterm and the final were about 60%, but it was curved up so the average was in the B+/A- range. This was reasonable, because Professor Juneja prefers to give you problems that really make you think rather than questions that are simply obvious if you know the material. If you think you did awful on the exam, don't drop the class until you find out the average.

This man is a good and articulate teacher but rather intense for someone who is not a SEAS student and wants to just an advanced knowledge of statistics. Dont let the "introduction" bit fool you, within a few weeks you'll be in deep s$$$ if you don't keep up with the substantial amount of material covered everyday. I had some problems with family in the middle of the semester and had to leave for a week and when i came back i was absolutely lost in the class and he was absolutely unyielding about giving me an incomplete. On the other hand I had a friend in the class who was a freshman stats major and did just fine because he was regular and dedicated. Last thing: theres like 5 tvs in a 40 person class and he keeps calling to an invisible technician to change the focus of the camera so that the video (for students who are taking the class from home) can keep up with him. Its definitely surreal.

#### Workload:

Intense (for a CC econ major). Problem sets every week, a midterm, a final.

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