0

Suppose two teams play a series of games, each producing a winner and a loser, until one team has won two more games than the other. Let G be the total number of games played. Assume each team has a chance of 0.5 to win each game, independent of the results of the previous games.
(a) Find the probability distribution of G.
(b) Find the expected value of G.

I couldn't make much of a headway so I can't include what I have tried to do?

kris91
  • 401

1 Answers1

1

We will denote $F_{G}(g)$ as the cdf of $G$.

Hints:

  1. If $g<2$ then $F_{G}(g)=0$

  2. It suffices to find $F_{G}(g)$ for $g=2,3,4\ldots$

  3. If the game ends after$g$ turns then in the first $g-2$ games we have a tied result (note that the game can't end after an odd number of turns)

  4. The same team won the last two games

Belgi
  • 23,150