You are playing a game at a carnival. You can win $5 with probability 0.15 on each round, but if you lose, you pay $2. Assume each round that you play is independent of the others. Let X be the number...

Extracted text: You are playing a game at a carnival. You can win $5 with probability 0.15 on each round, but if you lose, you pay $2. Assume each round that you play is independent of the others. Let X be the number of rounds it takes for you to get your first win (including the first win). X is distributed [ Select ] The expectation of X is [Select ] If you stop playing after your first win, your expected winnings (i.e. net profit, or the number of dollars you win or lose from playing the game; positive if you win more money than you lose) is [ Select ] You are playing a game at a carnival. You can win $5 with probability 0.15 on each round, but if you lose, you pay $2. Assume each round that you play is independent of the others. Let X be the number of rounds it takes for you to get your first win (including the first win). X is distributed [ Select ] [ Select ] The expectation of X Geometric(p = 0.15) Exponential(\lambda = 0.15) If you stop playing aft number of dollars you winnings (i.e. net profit, or the Poisson(lambda = 1/0.15) %3D me; positive if you win more Binomial(n, p = 0.15) money than you lose) You are playing a game at a carnival. You can win $5 with probability 0.15 on each round, but if you lose, you pay $2. Assume each round that you play is independent of the others. Let X be the number of rounds it takes for you to get your first win (including the first win). X is distributed [Select ] The expectation of X is [ Select ] [ Select ] If you stop playing after number of dollars you w innings (i.e. net profit, or the e; positive if you win more 20/3 1.5 money than you lose) is 3/20 2/3 You are playing a game at a carnival. You can win $5 with probability 0.15 on each round, but if you lose, you pay $2. Assume each round that you play is independent of the others. Let X be the number of rounds takes for you to get your first win (including the first win). X is distributed [Select] The expectation of X is [Select] If you stop playing after your first win, your expected winnings (i.e. net profit, or the number of dollars you win or lose from playing the game; positive if you win more money than you lose) is [ Select ] [ Select ] -2 -19/3 Question 15 O pts 20/3


Extracted text: Part 2: Let's say a friend of yours begins playing the game as well; your friend has a 0.2 win probability. Let Y be the number of rounds it takes for your friend to get their first win (including the first win). Assuming that X and Y are independent, what is the probability that your friend wins before you do (i.e. what is Pr(X >Y)? Note: This is a challenging question. No point is assigned to it. O (1 – py) – (1 – px) = 0.05 We do not have enough information to answer this question. 3 1 1 5 PX PY (1-px)PY 1-(1-ру)(1-Рx) 2 0.531