Comments on Final:  Took ~90 minutes to complete.  I checked my answers with the solutions after the exam.  I'll give you the answers I have that didn't fit the solutions or to problems whose solutions weren't written yet.

Problem 1:  Good problem.  One quick thing, in the example, we say for all n in N but we don't in the actual problems -- should we either remove it from the example to be consistent (since in the problem description, we are already told that the domain of discourse is N). 
Took 4 minutes.

Problem 2:  Another good one.  
Took 3 minutes (mostly taken to write up the explanation)

Problem 3:  Do we define partially ordered coordinatewise vs. ordered lexicographically?  i forgot the first one so didn't get that one.  Other than that, part a was fine.  Part b was fine too.  I assume most students will probably pick to use c+s vs. the lexicographical ordered pair.  For part c, it seems this could be a bother to grade since it's so openended and students can prove it numerous ways.  I used the connected and acyclic definition of trees and it was easy using that def and structured too.  I'm afraid that we may get a lot of hand-wavy arguments.
Took 14 minutes.

Problem 4:  Do we define a losing strategy?  Is it just basically a strategy you follow to guarantee you lose?  In part e, there is some wording issues -- it says "if neither player has a non-losing strategy not have a winning strategy" -- should just say "if neither player has a non-losing strategy"?  If i were to pick 5, I would probably pick a, b, e, f, g.
Took 6 minutes.

Problem 5:  Part a was fine -- 11!/2!3!.  Are we going to mention somewhere they can leave their answers with factorials and choose notation, etc?  Part b was also fine -- 11!/2!3! - 9!/2! - 9!/3! + 7!  Are these right?
Took 5 minutes.

Problem 6:  I like this problem alot!  Part a was fine.  Part b - i ended up using stars and bars and got (2^11-1+2 choose 2).  Which made part c easy.  
Took 7 minutes.

Problem 7:  Part a -- wording:  we mean to say "before Carol picks two goats", not "before Carol picks a goat".  Part b was fine too.  I did it with a tree and got w=1/2.  Part c was just like in pset problem.
Took 9 minutes.

Problem 8:  Everything looked okay.  
Took 7 minutes.

Problem 9:  I had a lot of trouble with this one.  I couldn't get part a to converge.  I ended up with Sum(1->infinity) {n/Sum(1->infintity){1}} -- and I don't think this converges.  But i'm not sure since all these sums got me a little confused.  Part b I got something similiar to part a for E[R^2] and i think it does not converge so it works out here.  I gave up after a while.
Took 10 minutes.

Problem 10:  The expectation formula we use all the time for MTF is actually the third in the appendix isn't it?  (the one where R must be natural number based?).  Used Wald's and it came out fine.  Maybe for part b, we should ask for the closed form.  Otherwise, I feel like some students may give a ugly sum and hand wave why we should be able to find a closed form.  The first formula I came up with involved flooring exponents and looked ugly.
Took 8 minutes.

Problem 11:  Good problem.  SHould state the bernoulli has probability p of being 1.  
Took 2 minutes.

Problem 12:  I choose the first one because i rememebered it from the in-class problems and I think it was the one that my table actually got to.  I think it's shorter than the other proof will be.  Both won't be too bad though.  
Took 3 minutes.

Problem 13:  It took me a while to understand what this problem wanted but it looks like what I have right now is a draft and will be revised on wording?  OTher than that, a basic application of pairwise sampling.
Took 5 minutes.


OVERALL:  The length is fine i think.  I did however recognize a lot of the problems, if not from this term, then from past terms.  It seemed pretty heavy on the last half of the term -- everything from problem 5 on were on counting/probability/etc.  There is no structural induction like albert promised :)