You and your friend are taking turns playing a game; two hands are played in each round. You play the first hand of the round and your friend plays the second hand of the round. Each hand has a net gain distribution, Mi, described by the following PMF: ??(?) ={1/4 ? = −1 1/2 ? = 0 1/5 ? = 1 1/20 ? = 1.5 0 ??ℎ?????? } It is fair to assume that net gains in different hands and/or rounds are independent and outcome of ? ≤ 0 is a loss. .a. What is the PMF of the total number of rounds until the first time that your win is immediately followed by your friend’s loss? b. What is the expected number of rounds until each of the players has “won” (? ≥ 0) at least once? c. Your friend leaves and you are left to play the game by yourself (somebody takes your friends place, so you still play only one hand per round). You decide to stop playing once you have won at least once with net gain of ? = 1 and ? = 1.5. How many hands are you expected to play?
You and your friend are taking turns playing a game; two hands are played in each round. You
play the first hand of the round and your friend plays the second hand of the round. Each hand has
a net gain distribution, Mi, described by the following PMF:
??(?) ={1/4 ? = −1
1/2 ? = 0
1/5 ? = 1
1/20 ? = 1.5
0 ??ℎ?????? }
It is fair to assume that net gains in different hands and/or rounds are independent and outcome
of ? ≤ 0 is a loss.
.a. What is the PMF of the total number of rounds until the first time that your win is
immediately followed by your friend’s loss?
b. What is the expected number of rounds until each of the players has “won” (? ≥ 0) at least
once?
c. Your friend leaves and you are left to play the game by yourself (somebody takes your
friends place, so you still play only one hand per round). You decide to stop playing once
you have won at least once with net gain of ? = 1 and ? = 1.5. How many hands are you
expected to play?
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
