StatsG0d

It depends. Yale has a very small program but Columbia's is quite sizable. More than anything, I would say the Ivies are heavily international in terms of their PhD student body. It's difficult to compete with people going to Peking University in China when you went to a state school in the US. Not too sure regarding your second question. I'd imagine Berkeley and Washington are similar because they are very top tier programs. UNC I doubt is anywhere near as competitive.

I think Emory would be tough given the English ability. They seem to care a lot about that. In their application, they have a component where you have to record a 1:30 video about why you want to study Biostatistics.

I would say you've got a good chance to get into a good PhD program. I would maybe add on a few of the larger state schools like Penn State, Purdue, and Texas A&M (all of which have machine learning faculty in their stats departments). The Ivies are pretty tough to break into, especially for a PhD. So if you're interested in a PhD, definitely take off a few of those and add on some more realistic schools. On the other hand, I feel Virginia might be a little "too safe". As everyone says, your advisor matters more than ranking, but I still think it helps. Just do some research on good programs that have faculty that do machine learning. For the MS, I would say you have a very good shot at getting into any of those schools. I don't think your work experience will help unless you're doing some type of research (perhaps in applied statistics).

Your grade in Analysis will carry more weight anyway but it was just a thought. Maybe consider applying to A&M or NCSU (or some other larger state school department)

Unfortunately, I don't see how that could help. The committees might be forgiving on Calc 3 if you say something like it was taken freshman year and it was difficult to get used to the college lifestyle of something (of this I'm not certain). But there's not going to be much of a defense for Complex Analysis. I would advise against saying you didn't study for a class on your personal statement to justify your grade. I'm confident you'll get in somewhere, just be rather cautious about where you apply.

I think at the very top they do care. Depending on what you're learning, there's not too much from even Real Analysis (I) that's helpful in probability. However, it shows one's ability to do theoretical and abstract math, so regardless of whether it's "useful," in terms of a prerequisite, it's useful as a tool for admissions. I'm by no means saying the OP doesn't have a shot, but it's not a shoe-in either. That's why I would advise the OP to apply to a few top 7 schools as well as a few (non-Ivies) in the 8-20 range.

I think you have a pretty good shot at the MS programs, but I think your mathematical breadth will bar you from most PhD programs. You could try to target schools that will automatically consider you for masters if you get rejected.

Of those schools, I'm confident you'd have a good shot at Penn State. Yale is (very) difficult to get into. I think they prefer that applicants take (and do well in) the math GRE. I'm not too familiar about the other programs to give you information. Regarding the other question, I think it depends on how forgiving committees are with the B+ in Complex Analysis. In my experience and from those I've heard about, it is extremely difficult to crack the top 7, but after that it becomes significantly easier. Letters could make a big difference though.

I think you might have a shot at places like South Carolina and Kansas State. I agree with everyone else saying that the other programs might be difficult. Florida may be a possibility because they have a real analysis course in the first year curriculum for those who haven't taken it yet, and I think a lot of other schools admit qualified students who haven't taken real analysis, forcing them to take it in their first year. That being said, I agree that school reputation matters and that not having taken real analysis is a serious detriment taking this into account. A 161Q is pretty sufficient for a MS, but I'd say this score given your math background will almost certainly exclude you from a PhD program. I'd probably advise against applying to some of those schools, as some do not really distinguish between Master's and PhD admissions (everyone is admitted to the PhD program if admitted, and the first year curriculum is identical). You should probably research this to find out which schools do this.

I don't really think you'll need to retake the GRE, for most of those schools (maybe for Washington it would help). For the others, I think you have a very good shot at getting into a few of them. Penn State DOES consider the writing score of the GRE, and a 5 is certainly a strong score in that regard. My only concern would be your C in probability theory (was it measure theoretic?). But otherwise, your profile is very strong.

Your profile is pretty similar to mine when I was applying (research experience, grades, etc.). Frankly, I think the list of schools you put is much too top-heavy. I applied to UCLA and Columbia of those schools you listed, and was ultimately waitlisted to UCLA and rejected from Columbia (but accepted for their non-funded MS). As cyberwulf mentioned, you'll want to add in at least a few schools in the 15-25 range. Sometimes results can surprise you (both in good and bad ways).

I know that at my program, they haven't begun looking at applications yet (I believe they wait until after the deadline).

For the first year sequence in probability, my program uses Casella and Berger's Statistical Inference. The first few chapters are devoted to probability theory, while the rest of the book is primarily mathematical statistics.

I think you would be fine with either choice. The only advantage you MIGHT get from the stats class is maybe some other university you apply to will give you credit for that class so you wouldn't have to repeat it. Having said that, the measure theory course would be looked upon very favorable by admissions committees. It's a really tough call in my opinion. I guess if I were you, I'd go with the grad analysis class.

Have you read They go pretty in depth about the SOP. In general, though, you shouldn't be too specific about your research interests. You don't want to come off as naive. I usually picked 2-3 subspecialties that seemed interesting to me and mentioned some faculty members in each area.

The Manhattan Strategy Guides are also very good. They teach you some quick tricks you might have forgotten. Good luck.

I think you've got a pretty great shot at almost anywhere. wine in coffee cups said it best about the idiosyncratic programs. I've been subject to their idiosyncrasies myself. I would definitely at U Chicago onto the list and maybe Purdue, who places a heavy emphasis on computation (which I assume you're interested in due to your engineering/computer science background.

I would probably retake the GRE if you have the time/money. I've spoken with an admissions officer and she said that they do actually consider the GRE/GPA by itself before even considering the whole application. In regards to schools, maybe the masters will help but I think the various B grades you've gotten might hurt you a little bit despite the decent GPA. Plus, graduate GPAs tend to be higher than undergrad GPAs. I think Bayesic's list of schools are decent but I think Penn State and UCLA are reaches and not targets. UCLA is pretty tough to get into given its location (I was rejected from there, and I was accepted to some schools in the reach list he provided). You may wish to broaden the range of schools to include schools like Michigan State, for example.

Does your GPA actually transfer? I always thought that transfer students start with no GPA and the GPA they graduate with refers to all classes taken at that university?

I would be pretty surprised if you got rejected to any of the statistics programs you mentioned. NCSU is very good, and about tied in rank with Michigan and Texas A&M. While I was rejected from the former, I was accepted to the latter. Your profile looks much better than mine, so I would say maybe apply to a couple in the top-5 and 3-4 in the top-10. I would wipe UCSB and Rice off of your list unless you are interested in financial time series.

I second this.

For statistics, I personally don't really think it will be a huge detriment. I think you are probably better off taking a high-level math course than some programming course, especially if your programming skills can be showcased in other ways (other classes, projects, etc.--things you can mention on your personal statement).

I would think that it matters. A lot of people tend to agree that undergrad quality matters. By extension, I think that it at least has some impact.

The cost of living in Blacksburg is decent, but the cost of living in West Lafayette is about 15% below the national average. You can get 2 bedroom apartments for 600-700 per month, making your share only 300-350 per month. Blacksburg, with its proximity to DC, has much higher rent than West Lafayette. This may or may not be offset by the funding factor.

I would probably go with Purdue. As you said, there are a lot of diverse research interests. It's also VERY cheap to live in West Lafayette, so that might mitigate the extra semester of tuition.