Consider the following game in which a fair coin is repeatedly tossed. The rules of the...
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Consider the following game in which a fair coin is repeatedly tossed. The rules of the game are straightforward. You win a $1 when you get two heads in a row for the first time. However, you have to pay $k for each toss. For instance, if it takes you 10 tosses to get two heads in a row for the first time, then your profit and loss (PL) is $1$10k. However, the number of tosses that will take you to win a $1 is uncertain, which is denoted by a random variable X. Hence, in reality your PL is stochastic and can be described as PL = $1 X x $k for some fixed cost k and random variable X. By expectation, what is the maximum price you would be willing to pay per a coin toss? In other words, what is the value of k that makes the game break even? Use a MC simulation to answer this. (7 Points) Hint: Breaking even means that the expected value of the PL is zero. Your task, hence, is to find the value k that leads to E[PL] = 0, which requires finding E[X]. Consider the following game in which a fair coin is repeatedly tossed. The rules of the game are straightforward. You win a $1 when you get two heads in a row for the first time. However, you have to pay $k for each toss. For instance, if it takes you 10 tosses to get two heads in a row for the first time, then your profit and loss (PL) is $1$10k. However, the number of tosses that will take you to win a $1 is uncertain, which is denoted by a random variable X. Hence, in reality your PL is stochastic and can be described as PL = $1 X x $k for some fixed cost k and random variable X. By expectation, what is the maximum price you would be willing to pay per a coin toss? In other words, what is the value of k that makes the game break even? Use a MC simulation to answer this. (7 Points) Hint: Breaking even means that the expected value of the PL is zero. Your task, hence, is to find the value k that leads to E[PL] = 0, which requires finding E[X].
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To find the value of k that makes the game break even we need to find the expected value of the PL a... View the full answer
Related Book For
Probability and Statistics
ISBN: 978-0321500465
4th edition
Authors: Morris H. DeGroot, Mark J. Schervish
Posted Date:
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