Exam 7: Expectations and Decisions

In order to make a decision using the minimax criterion, we select the action that gives the _______ of the _______ opportunity losses.

Calculating the mathematical expectation requires having the values for the amounts and their corresponding _______.

Given the profit payoff table below, if we use the maximin criterion we will choose action _______.

You are given two states of nature $S 1$ and $S 2$ and two courses of action $A 1$ and $A 2$ with a profit payoff table. -Using the table above, answer the following: If the probabilities of $S 1$ and $S 2$ are, respectively, $\frac{4}{5}$ and $\frac{1}{5}$ , the expected profit if $A 1$ is selected is

A salesperson must choose between a straight salary of $\$ 25,000$ and a salary of $\$ 20,000$ plus a bonus of $\$ 8,000$ if his sales exceed a certain quota. How does he assess his probability of exceeding the quota if he chooses the lower salary with the possibility of a bonus?

What is Bayesian analysis?

If the payoffs are losses or costs, the optimistic decision maker would use the minimax criterion.

A grab-bag contains 6 packages worth $\$ 2$ each, 11 packages worth $\$ 3$ each, and 8 packages worth $\$ 4$ each. Is it reasonable to pay $\$ 3.50$ for the option of selecting one of these packages at random?

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 minimin criterion to the amount of money he will have to pay?

The expected value with perfect information is calculated by subtracting the maximum expected profit under uncertainty from _______.

If the payoffs are quantities such as losses or costs, which we want to make small, we use the minimax criterion.

Two finalists are in a tennis match with the winner to receive $\$ 40,000$ and the loser $\$ 25,000$ . What are the two players' mathematical expectations if their probabilities of winning are $\frac{2}{3}$ and $\frac{1}{3}$ ?

For a payoff table containing company profit values, an optimistic manufacturer would most likely use the _______ criterion.

You are given two states of nature $S 1$ and $S 2$ and two courses of action $A 1$ and $A 2$ with a profit payoff table. -Using the table above, answer the following: The action which maximizes expected profit is

When applying the _______ criterion, we look for the largest value of each column of the payoff table and select the largest of these column values.

Suppose the mathematical expectation is given with the corresponding probabilities and all amounts but one amount $a$ . Solving for $a$ requires $E$ to be multiplied by a number.

When calculating the mathematical expectation, amounts which represent losses are assigned _______ values.

Two finalists are in a tennis match with the winner to receive $\$ 40,000$ and the loser $\$ 25,000$ . What are the two players' mathematical expectations if they are equally matched?

If the amount that the consultant is paid is reduced by a penalty which is 20 times the size of the error, the prediction which maximizes his payment is

If the amount that the consultant is paid is reduced by a penalty which is 20 times the square of the size of the error, the prediction which maximizes his payment is