Waiting times for coin-flipping patterns (use a martingale argument)

[Win_odd Dhamnekar]

My answers:

In my opinion, answer to (a) is $$\mathbb{E} [N] = p^{-4}q^{-3} + p^{-2}q^{-1} + 2p^{-1}$$In answer to (b), X_N is wrong. It should be X_N=p^-4q^-3 - p^-3 q^-2- p^-2 q^-1 - p^-1.

This might be a typographical error.


Is my answer to (a) correct?