04-27-2006, 03:20 PM

Joe and Bob are playing chess. Joe wins with probability p and Bob wins with probability q and finally the game is a tie with probablity 1-p-q.

I got the Probability Mass Function of the number of games they would play as:

P(X=x) = (1-p-q)^(x-1) (p+q)

I need the expectation of the number of games. So far I have:

(p+q) Summation from 1 to infinity of x (1-p-q)^(x-1)

I was told that I need to take the intergral of this to form a ore managable equation but I'm still stuck. Please help.

I got the Probability Mass Function of the number of games they would play as:

P(X=x) = (1-p-q)^(x-1) (p+q)

I need the expectation of the number of games. So far I have:

(p+q) Summation from 1 to infinity of x (1-p-q)^(x-1)

I was told that I need to take the intergral of this to form a ore managable equation but I'm still stuck. Please help.