Suppose two teams play a series of games, each producing a winner and a loser, until one time has won two more games than the other. Let \(G\) be the number of games played until this happens. Assuming your favorite team wins each game with probability \(p\), independently of the results of all previous games, find:

- \(P(G=n) \) for \(n=2,3,\dots\)
- \(\mathbf{E}(G)\)
- \(\mathrm{Var}(G)\)

[Pittman p220, #18]