MathCat

Based on what's here, I'd say B for the networking opportunities and seeing new perspectives. Do you have a personal preference for the two? Is a smaller cohort more or less appealing to you? Do you have a strong location preference? Preference for the atmosphere at either place (if you've visited)? The extra funding that a wealthy private institution has can be very helpful for things like funding flexibility (e.g. continuing to fund you for an extra year if you don't finish on time), perhaps more support for conferences, etc. Have you looked into the job placements of graduates? Is either program better at placing graduates in the careers you want?

Go where the funding is, I'd say. Doing a masters may also help your PhD applications down the line.

I really do think that the new perspectives and networking benefits of going to Stanford are worth something. However, I can't know your desire for probability vs. statistics, which is obviously an important factor.

There might be ethics violations if you are a roommate with somebody you are TAing or grading for. I think it's unlikely to arise, as you said, but you need to be aware of whatever rules the university has if it does come up.

Even if you want a research career, TA experience is good to have. Perhaps not having to TA, or having a low workload is good, but the opportunity to teach or TA if I wanted to is something that I would require in a program, just for job prospects.

Waterloo is also 1 year, at least in pure math. Their funding is also generally the best of those 4 (but the department is the least prestigious). UBC and Toronto don't offer much funding considering the cost of living in Toronto or Vancouver, but it is a livable. Places like Waterloo or Western Ontario are a bit more generous. UAlberta also has a minimum funding guarantee, but I think it's only $15,000 or something. Still, I think the landscape in Canada is much better for funded Masters programs, in that almost everyone admitted to a research-based program (which should include all or almost all math and stats programs) will get funding, with enough to live on after tuition, if a waiver is not included. Funding is generally a bit worse for international students, because some places don't increase the funding package, but your tuition will be a few thousand more. I know Waterloo does offer more funding for international students to offset this, but I believe UBC does not. Toronto waives tuition so it doesn't matter.

I would imagine it depends on the person, as would any roommate. edit: I guess one possible concern is that they not be a student you could end up TAing for.

It would be fine to ask for an extension, but be prepared for the possibility that they will say no.

I would make it shorter. I'm assuming he already has this information about you overcoming obstacles and now performing well. I would just say something like "I am writing to reiterate my interest in your program." with perhaps another sentence to open or close it. I would not mention anything about it being a "life-changing opportunity" - comes across a bit cheesy to me, even if it is honest. Keep it concise and professional.

I wouldn't actually ask them to review it faster. Instead, I'd email to say you have an offer with an urgent decision deadline, but are still interested in their program. However, only send this if you are actually interested in their program. You did say the offer you have is one of your top choices - are the ones you're waiting on higher on your list?

Definitely contact ASAP, but as you said, there is a (pretty good, I think) chance that the spot is no longer available.

Top 15 vs. top 50 is a significant difference if you want to go into academia. Since you didn't list a really compelling reason to go to the top 50 one (e.g. top 15 unfunded or something), I'd recommend you take the top 15 offer.

An OGS is a 1-year award normally. You should not expect a renewal, but funding from a different source (e.g. TA).

Are you certain the prof at Berkeley would take you?

I've certainly heard some unpleasant things about the atmosphere in the PhD program at Berkeley, but perhaps you know better, since you're there. The closer knit atmosphere at Stanford would be my preference as well, but that's a personal choice. Stats vs. probability is your own call, I don't think anyone can help you there. No matter what you choose, you are going to a good place. You can't make a horribly wrong call here.

I'd say Stanford based on you doing undergrad at Berkeley, and also more flexibility with advisors. It's also possible you'd be exposed to new takes on things and develop interests in new directions by changing schools. However, these are not really strong reasons. Do you have a preference for personal fit or location?

Do you have the ability to support your family without a stipend? Even the $8000 UNH is offering is not enough for that.

If you want to go to a top 10 program, apply to several (that are good fits). I was kind of pessimistic and chose more in the range I felt like were safer bets (top 15-30), and got into those. I only applied to 2 of the top 10-15 and didn't get in. Perhaps if I had applied to more I would have gotten into one. I would recommend people take a different approach than I did. Your GPA and where you're coming from both sound competitive for top programs. It depends on your LORs, research experience, and fit I think. Perhaps ask the profs writing your LORs if they think you're being realistic or not. I think you should apply to some top programs anyway, but perhaps pick a few lower ranked places to apply to as well (but only ones you'd still go to, and that would be a good fit).

I'm not convinced that the ranking of your undergrad institution will hold you back if you have good GPA and letters of reference. I went to a pretty lame school and got into some highly ranked programs. I think this is because my LORs were very strong. I also don't think you should rule places out because of GRE, unless you know for sure that they have minimum cutoffs that you don't meet. A lot of places don't place much stock on the GRE, and it could depend how the faculty on the adcomm view it. If you want to go somewhere, you should apply. Depending on your field, research experience is a plus but not always necessary. (For example, in math, many tip-top programs explicitly state that they don't expect you to have research experience already.) If you have some, and can get strong LORs from profs that supervised it, I think that helps a lot though, especially if you have a numbers weakness you need to overcome (e.g. low GPA, GRE). You have to figure out what you are looking for in a grad program. It's helpful to narrow it down a bit by ranking, as appropriate for your long term goals (e.g. I didn't want to go to the US unless the program was ranked better than the programs I could get into in Canada), just because there are so many programs to choose from, in general. From that, start looking at which meet your criteria - things to consider include personal fit (would you want to live there?), research fit, success of graduates in the career path you want, etc.. Again: if you find a place that is a good fit for your interests and you really want to go, you should apply. Don't hold back just because you think it's a long shot. More specific advice would require you to be more specific about your profile and field.

You still have a couple of days. If you must accept and then possibly rescind, wait as long as you can until accepting.

Definitely don't waste much space with an introduction, but even one sentence about your goals is good.

The school I accepted is pretty much tied for the highest ranked I got into, but it is not the most prestigious (people think it's lower ranked than it is, generally speaking). But that wasn't really the deciding factor for me. It was the best personal fit, tied for best research interest fit with program X, and the graduates do much better than those from X.

It worries me a bit, but did not stop me from accepting an offer there.

It seems like you might be telling them a lot of things that they could see elsewhere on your application. Is there a CV included in the application? If so, try not to replicate information, because the space in your SOP is precious. It seems like all but the first sentence of your second paragraph could be somewhere else in your application, but this depends a lot on what you get to include. You are giving a lot of information, but not really saying much about yourself or your interests. Why do you like the subjects you are interested in? You mention a specific course piqued your interest, but what about it? You say "Both professors and their scholarly work, fit my interests and eventual goal for my doctoral work.", but you never actually described your interests or goals, you just listed what you had worked on or are working on. You should be more explicit about your interests, goals, and how this makes you a good fit. More of an introduction would be good. Personally, I used a (brief) introduction as a place to talk about my goals. Your SOP starts rather abruptly. p.s. Are you really applying for Fall 2015 (i.e. to start in Fall 2015)? The application season is over at this point...

I would suggest explaining the situation to school X and asking for an extension. It's better to act in good faith first. Only accept the offer with the possibility of rescinding for Y's offer if they say no. It's better to be upfront and honest - maybe they'll be accommodating, and you won't have to risk burning any bridges.