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INTRODUCTION To Statistical Decision Analysis, 28 Aug, 2014
SUMMARY The expected value of X, E(X), is found by multiplying each of all the different possible values of X by its probability of occurrence and adding the products. Thus, E(X) = I,Xp(x) If the X's are monetary values such as dollars, then E(X) is called expected monetary value EMV. The EMV decision criterion for choosing an action from…
PROBLEMS 1. A firm can make a product and sell it, or buy it from a wholesaler and sell it. Payoffs have been computed and are given in Table A. which shows, for example, that a profit of $50,000 will be realized if the firm makes the product and customer demand is high. The firm think s the chances…
UTILITY AND THE EXPECTED UTILITY CRITERION
UTILITY AND THE EXPECTED UTILITY CRITERION Utility is a measure which quantitatively expresses a decision maker's attitudes toward chance situations. In thi.: section we shall show how dollar payoffs for decision problems can be converted to correrxmding utWty measures. Then the choice of action can be ~etermined by using expected utility value EUV in place of expected monetary value.…
CERTAINTY EQUIVALENT FOR A CHANCE SITUATION
CERTAINTY EQUIVALENT FOR A CHANCE SITUATION In the conversation recorded earlier, Fran said she would be willing to toss a coin to decide between a $20,000 settlement and going to court; she was indifferent to that choice. To Fran $20,000 for certain is the same as, or equivalent to, an 80-20 chance at $40,000 or – $10,000. We…
EMV MAY NOT BE A SATISFACTORY CRITERION
EMV MAY NOT BE A SATISFACTORY CRITERION This section opens with a conversation which shows that a person may choose not to use the EMV criterion In making a decision. In foliage sections we shall discuss a procedure that can be used to solve a decisions problem when EMV is not acceptable to the decision maker. Fran: Dan, renumber that law…
DECISION TREES FOR EMV CRITERION
DECISION TREES FOR EMV CRITERION The first step in analysis by a decision tree is to construct a "bare" tree. A bare decision tree is used to describe the sequence in which actions must be taken and chance events willoccur. Let's use the earlier retail store buyer example to introduce the procedure. Figure 6.3 shows the bare tree.…
THE EMV DECISION CRITERION
THE EMV DECISION CRITERION The possible consequences of various courses of action are called payoffs Medical doctors may use numbers of years of prolonged life as the possible payoffs for different methods of treating a disease. Political candidates may use numbers of votes as payoffs. Thus, what a decision maker considers as being payoffs depends upon the decision maker's…
PROBLEMS 1. A retail store receives 3,4, 5, or 6 telephone orders per hour with respective probabilities of 0.1, 0.4, 0.3, and 0.2. la) Compute the expected number of calls per hour. (b) Estimate the number ol calls received in a 50-hour business week. 2. A salesperson sells 0, 1, 2, 3, 4, 5, or 6 stereo systems…
Expected Monetary Value
Expected Monetary Value When the numbers being averaged are in monetary units, say, United States dollars, expected value is often referred to as expected monetary value and symbolized by EMV. It is computed in the same way as other expected values. EXAMPLE A fire insurance company assigns a probability of 0.001 that a particular type of building…
Use of Tree Diagrams The next example shows the use of a tree diagram to convert an expected value problem into workable form. EXAMPLE On the first visit with a customer, a salesperson sells either 2″ or 0 cases of a product with probabilities, respectively, of 0.2, 0.3, and 0.5. A second visit is made if 0…
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