I am still working on this problem, but I want to propose something to think about. It seems to me there are two situations that could happen. Barack could come first, or Hillary could come first.
From here, can I sum the:
the expected value of hillary's time waiting given hillary came first, and the expected value of barack's waiting time given barack came first?
I am sort of wondering if it matters who came first. I intuitively at least want to consider it, but am unsure how that all pans out.
