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 firstwin). 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 thenumber of dollars you win or lose from playing the game; positive if you win moremoney 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 firstwin). X is distributed [ Select ][ Select ]The expectation of X Geometric(p = 0.15)Exponential(\lambda = 0.15)If you stop playing aftnumber of dollars youwinnings (i.e. net profit, or thePoisson(lambda = 1/0.15)%3Dme; positive if you win moreBinomial(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 firstwin). X is distributed [Select ]The expectation of X is [ Select ][ Select ]If you stop playing afternumber of dollars you winnings (i.e. net profit, or thee; positive if you win more20/31.5money than you lose) is3/202/3You 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 roundstakes for you to get your first win (including the firstwin). 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 thenumber of dollars you win or lose from playing the game; positive if you win moremoney than you lose) is [ Select ][ Select ]-2-19/3Question 15O pts20/3 Part 2:Let's say a friend of yours begins playing the game as well; your friend has a 0.2 winprobability.Let Y be the number of rounds it takes for your friend to get their first win (includingthe first win).Assuming that X and Y are independent, what is the probability that your friend winsbefore 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) = 0.05We do not have enough information to answer this question.3115PXPY(1-px)PY1-(1-ру)(1-Рx)2 0.531

Question

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 firstwin). 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 thenumber of dollars you win or lose from playing the game; positive if you win moremoney 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 firstwin). X is distributed [ Select ][ Select ]The expectation of X Geometric(p = 0.15)Exponential(\lambda = 0.15)If you stop playing aftnumber of dollars youwinnings (i.e. net profit, or thePoisson(lambda = 1/0.15)%3Dme; positive if you win moreBinomial(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 firstwin). X is distributed [Select ]The expectation of X is [ Select ][ Select ]If you stop playing afternumber of dollars you winnings (i.e. net profit, or thee; positive if you win more20/31.5money than you lose) is3/202/3You 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 roundstakes for you to get your first win (including the firstwin). 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 thenumber of dollars you win or lose from playing the game; positive if you win moremoney than you lose) is [ Select ][ Select ]-2-19/3Question 15O pts20/3 Part 2:Let's say a friend of yours begins playing the game as well; your friend has a 0.2 winprobability.Let Y be the number of rounds it takes for your friend to get their first win (includingthe first win).Assuming that X and Y are independent, what is the probability that your friend winsbefore 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) = 0.05We do not have enough information to answer this question.3115PXPY(1-px)PY1-(1-ру)(1-Рx)2 0.531

Accepted Answer

Since you have asked multiple questions, we will solve the first question for you. If you want any…