Think long and hard before taking this class. Not because it's bad, but because it requires a serious commitment of your time and effort. This class is really two classes in one -- it covers two semesters of material (all of 3105/4105 and all of 3107/4107) plus the classes are 2hr 45min twice a week. Also, it's impossible to get ahead of your work, because there's always another problem set due in just a few days (see the workload below). Of course, it's also worth six credits, so you'll be rewarded for your efforts, especially if you can pull off a good grade. But just appreciate how long you'll be spending in each class and doing problem sets and just generally doing probability/statistics.
In addition, IMO, the fact that this class goes at double-speed makes it more than twice as difficult. For example, if you were to ever miss a class or ever be unfocused during class, you're suddenly way behind. Furthermore, there's less time to let the often difficult concepts sink in before you've moved onto concepts which build on top of those concepts. If you're confused about anything, going to office hours is very important, otherwise you may stuck behind for a while.
Two other important details to realize about the class:
(1) It's almost entirely master's students, many of them getting master's in statistics. So the people in this class are bound to be pretty smart and you can't really count on much of a curve.
(2) It's fairly theoretical and proof-based. So it may be an an adjustment if you're not used to that type of course. Very few of the problem set questions or the exam questions were purely computational.
As far as Liam himself is concerned, I have a generally positive review. First of all, he's definitely a nice guy, and really does want people to come to his office hours. Second of all, he's very relaxed, especially as a lecturer, which can sometimes make it a little tough to focus for such a long time, but it also makes it a far more pleasant experience overall. Finally, he always gives a break at the halfway point in class, and more often than not finishes class early, sometimes even by a half hour.
I think he does a decent, but not spectacular job of teaching the material. He admitted on the first day that he's not as strong at probability (and especially combinatorics) as he is at statistics and I think that I may have, in fact, found things a bit clearer in the second half of the course. He goes at a pretty reasonable pace and always stopped to ask if there were any questions. One major flaw of his was that he sometimes kept things too abstract and failed to give more concrete examples to help clarify things. Additionally, though he repeatedly tried to get the class to participate, he usually failed, and classes ended up being almost entirely lectures. However, the fact is, this stuff is difficult and yet in the end, most students seemed to get it. I found that I ended up teaching myself some stuff from the textbook, but most of my understanding of the material came from the lectures. In particular, I sometimes found that Liam helped me get what was going on conceptually while the textbook helped with the actual steps that needed to be done (though the textbook wasn't great -- it may be worthwhile to use other statistics textbooks to supplement it).
Overall, I'd say you should take this class if you are either very into probability/statistics or need to get the statistics requirements very difficult. If you don't fit into one of these two categories, you may be better off taking 3105/4105 and then 3107/4107. If you've settled on taking 4109, Liam is a solid choice.