A 2-person game of target shooting is played in which each players takes a shot at a target in a sequential manner. If the player who starts the game hits the target, the player
wins right away. Otherwise, the opponent will take a turn. If nobody wins in the first
round, players continue to take turns and shoot at the target until one of them wins.
a) Suppose that Kayla’s probability of shooting the target is 1 while her opponent’s
probability of shooting the target is 2 where 2 >p1. The players agree that Kayla
always starts the game because she is the weaker player and they set a friendly stake
of $1 where the loser gives the winner $1 for each round he/she loses. Let’s denote by
the RV Kayla’s profit after games. Find the mean and the variance of .