M2 4. Suppose that Joe is playing the following version of the gambler's ruin problem. He startswith $50, and plays the game (in which he wins or loses $1 with probability 1/2 - 1/2)until he reaches $200 or loses all his money. Whenever he loses all his money, he goes tohis bank, borrows $50 again and starts playing again. If he reaches $200 then he stopsplaying forever.(a) Model the game as a Markov chain, describing the transition probability function.(b) Is it true that with probability one Joe will stop playing at some point? (I.e. thathe will hit $200.)

In this problem, we encounter a modified version of the gambler's ruin problem involving Joe. Joe…

Answered: 4. Suppose that Joe is playing the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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In a certain game, a player who bets $n either wins $2n (with probability 1/2) or loses the $n. So her total either increases by $n or decreases by $n, each with a probability of 1/2. A gambler uses the following strategy. She bets either $10 (if her total is $50 or more) or $5 (if her total is less than $50). If she starts with $100, what is the probability that she reaches $200 before losing everything?
Supposed a certain game is fair and costs $7 if you lose and has a net payoff of $10 if you win. The only possible outcomes of the game are winning and losing.
3. Player A has a $1 bill and a $20 bill, and player B has a $5 bill and a $10 bill. Each player will select a bill from the other player without knowing what bill the other player selected. If the total of the bills selected is odd, player A gets both of the two bills that were selected, but if the total is even, player B gets both bills. (a) Develop a payoff table for this game. (Place the sum of both bills in each cell.) (b) What are the best strategies for each player? (c) What is the value of the game? Which player would you like to be?
Suppose an oil company is thinking of buying some land for $950,000. There is a 60% chance of economic growth and a 40% chance of recession. The probability of discovering oil is 46% when there is economic growth and 34% when there is a recession. If there is economic growth and the oil company discovers oil, the value of the land will triple. If they do not discover oil, the value of the land will decrease by 10%. If there is a recession and the company discovers oil, the value of the land will increase by 50%. If they do not discover oil, the land will decrease in value by 75%. What is the expected value of the investment? Give your answer to the nearest dollar. Avoid rounding within calculations.
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Suppose an oil company is thinking of buying some land for $11,000,000. There is a 60% chance of economic growth and a 40% chance of recession. The probability of discovering oil is 46% when there is economic growth and 34% when there is a recession. If there is economic growth and the oil company discovers oil, the value of the land will triple. If they do not discover oil, the value of the land will decrease by 11%. If there is a recession and the company discovers oil, the value of the land will increase by 50%. If they do not discover oil, the land will decrease in value by 80%. What is the expected value of the investment? Give your answer to the nearest dollar. Avoid rounding within calculations. Select the correct interpretation of the expected value. O The expected value represents the mean investment value for a $11,000,000 land purchase. The oil company should invest in the land because, on average, the investment is profitable. O The expected value provides the total cost of…
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Avicenna, an insurance company, offers five-year commercial property insurance policies to small businesses. If the holder of one of these policies experiences property damage in the next five years, the company must pay out $26,500 to the policy holder. Executives at Avicenna are considering offering these policies for $497 each. Suppose that for each holder of a policy there is a 2% chance they will experience property damage in the next five years and a 98% chance they will not.(If necessary, consult a list of formulas.) If the executives at Avicenna know that they will sell many of these policies, should they expect to make or lose money from offering them? How much? To answer, take into account the price of the policy and the expected value of the amount paid out to the holder. Avicenna can expect to make money from offering these policies. In the long run, they should expect to makedollars on each policy sold. Avicenna can…
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Debra is buying prizes for a game at her school's fundraiser. The game has three levels of prizes, and she has already bought the second and third prizes. She wants the first prize to be nice enough to attract people to the game. The game's manufacturer has supplied her with the probabilities of winning first, second, and third prizes. Tickets cost $3 each, and she wants the school to profit an average of $1 per ticket. How much should she spend on each first prize? (Give your answer to the nearest cent.) Prize Cost of prize Probability1st 0.152nd $1.27 0.30 3rd $0.76 0.45
Avicenna, an insurance company, offers five-year commercial property insurance policies to small businesses. If the holder of one of these policies experiences property damage in the next five years, the company must pay out $23,600 to the policy holder. Executives at Avicenna are considering offering these policies for $791 each. Suppose that for each holder of a policy there is a 3% chance they will experience property damage in the next five years and a 97% chance they will not. (If necessary, consult a list of formulas.) If the executives at Avicenna know that they will sell many of these policies, should they expect to make or lose money from offering them? How much? To answer, take into account the price of the policy and the expected value of the amount paid out to the holder. O Avicenna can expect to make money from offering these policies. In the long run, they should expect to make dollars on each policy sold. O Avicenna can expect to lose money from offering these policies.…

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