Exam 7: Expectations and Decisions

A student wants to purchase a ticket to a very popular rock concert from a friend. He agrees to pay the friend $\$ 30$ , but will only get the ticket if he rolls a 5 or a 6 on an ordinary die, otherwise the friend keeps the ticket and the $\$ 30$ . What is the ticket worth to the student if he thinks that this arrangement is fair?

The following payoff table shows two surveys of data for the monthly rental prices for equivalent apartments in four different locations in a certain city. -Use the situation above to solve the following: A builder wants to construct apartments of the type referred to in the table and must select one of the four locations A, B, C, or D. Which location should he choose if he wants to maximize his minimum rental charge?

The annual income (in thousands of dollars) of all ten entries in a lottery are $30,25,50,48,30,30,60,42,38,15$ , and their chances of winning are all equal. -If we want to predict the annual income of the winner, what prediction maximizes the expected reward if the penalty is equal to 15 times the square of the size of the error?

An entrepreneur is considering building a new restaurant. She knows that if the restaurant is built and the economy improves there will be a profit next year of $\$ 70,000$ ; if the restaurant is built and there is a recession, there will be a loss next year of $\$ 10,000$ . If she buys a particular established restaurant and the economy improves, there will be a profit of $\$ 40,000$ next year; if she buys the established restaurant and there is a recession, there will be a profit of $\$ 8,000$ next year. -Construct a payoff table for the situation described above.

A speculator evaluating a particular investment concludes that, if the company's balance sheet claims are true, the speculator's profit will be $\$ 15,000$ , and if the company's balance sheet claims are false, he will lose $\$ 5,000$ . If he makes no investmentrbethas no or loss. -Suppose that the speculator's accountant feels that the spectator rates the accuracy of the balance sheet claims too low, that the probabilities of the claims being true or false are 0.30 and 0.70 . Would it affect the speculator's decision if he assigned these probabilities to the two events?

The values in the following table are the prices charged for three menu items at three different restaurants of equal quality: -Use the situation above to solve the following: A person who has narrowed his choice of entree to one of the three items is planning on dining at one of the three restaurants and will make his final choice of entree after having a cocktail. Which restaurant would he go to if he applied the minimax criterion to the amount of money he will have to pay?

A speculator evaluating a particular investment concludes that, if the company's balance sheet claims are true, the speculator's profit will be $\$ 15,000$ , and if the company's balance sheet claims are false, he will lose $\$ 5,000$ . If he makes no investmentrbethas no or loss. -In the situation above, if the speculator feels that the probabilities are above 0.20 and 0.80 that the balance sheet claims are true or false, respectively, what should he decide to do to maximize his expected profit?

In Bayesian analysis, we select the action which promises the _______ expected profit or the _______ expected loss.

If 600 lottery tickets are sold for a cash price of $\$ 150$ , what is the mathematical expectation of a person who buys one of these tickets for $\$ 1$ ?