4.4, 4.9(c) due on 10/31

Difficult
I was able to follow the coin example up until equation 11. Why is E(X) = E(X')? I'm guessing because their probabilities are equal, so does that mean that knowing the first toss is head makes no difference? Also, is the problem asking for the expected value of the length of runs of HEADS or TAILS? I assume we are looking at runs of heads out of convenience, but I'm not sure. The computation of the variance also confused me. I think it's because I haven't practiced it as much, but it was hard for me to follow.
Reflective
Aside from the above confusion, I found section 4.4 fairly straightforward since most of it relates to what we've already learned about conditional probability. It's nice to get a review of the material and also see it being applied in a different way. In section 4.9, I thought it was a little tricky since you had to think about writing p as np/n and realize that (1+ x/n)^n equals e^x. Otherwise, that example was also straightforward.