Re: How to do the homework?
@dudefromdayton, thank you for those examples of "offthecuff" reasoning (I assume that's an appropriate term). I ended up doing something similar on Homework 4, for lack of time. For example, I intended to try both analytical and bruteforce simulation approaches to solving #7 (which learning model has least outofsample error), but some other problems used up my time quota. So I employed roughandready reasoning, and got the right answer (I claim no victory, however, given the 20% chance of a random guess being right!).
I think it's a good idea to employ multiple methods, if enough time  mathematical analysis, numerical examples, simulation, graphical methods, even intuition. If they all produce the same answer, the problem is mastered; if not, then something needs fixing!
