Question: Consider two weighted coins. Coin 1 has a probability of 0.3 of turning up heads, and coin 2 has a probability of 0.6 of turning

Consider two weighted coins. Coin 1 has a probability of 0.3 of turning up heads, and coin 2 has a probability of 0.6 of turning up heads. A coin is tossed once; the probability that coin 1 is tossed is 0.6, and the probability that coin 2 is tossed is 0.4. The decision maker uses Bayes€™ decision rule to decide which coin is tossed. The payoff table is as follows:

(a) What is the optimal alternative before the coin is tossed?
(b) What is the optimal alternative after the coin is tossed if the outcome is heads? If it is tails?

State of Nature Alternative Coin 1 Tossed Coin 2 Tossed Say coin 1 tossed Say coin 2 tossed 0 0 Prior probability 0.6 0.4

Step by Step Solution

★★★★★

3.45 Rating (168 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a Say coin 1 tossed EP 060 04 1 04 Say coin 2 tossed EP 061 04 0 06 The optimal a... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

545-M-S-L-P (861).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

You are handed two coins, Coin S and Coin W. Coin S is a standard coin, with a 50% chance of turning up heads when its tossed. Coin W is a weighted coin with an 80% chance of turning up heads when...

In Problem 70, suppose that the coin is tossed n times. Let X denote the number of heads that occur. Show that P{X = i} = 1/n + 1 i = 0, 1, . . . , n Make use of the fact that when a and b are...

Suppose that in Problem 70 we continue to flip the coin until a head appears. Let N denote the number of flips needed. Find (a) P{N i}, i 0; (b) P{N = i}; (c) E[N]. Problem 70 Consider an urn...

Rena purchased 200 shares of a no-load stock mutual fund. During the year she received $3 per share in dividend distributions, and capital gains of $1,100 when she sold the stock after owning it...

A box contains 4 coins. Coin 1 is biased such that it comes up heads with probability 0.3. Coin 2 is fair, and equally likely to come up heads or tails. Coin 3 is biased such that it comes up heads...

1. The US. mint reports that some of the coins in circulation are in fact not fair, but others are fair. You ip a coin 100 times and it lands on heads 65 times. (a) Perform a hypothesis test by doing...

The U.S. mint reports that some of the coins in circulation are in fact not fair, but others are fair. You flip a coin 100 times and it lands on heads 65 times. (a). Perform a hypothesis test by...

1.An issue that will always be of interest to those that manage criminal justice organizations is one of continual hiring. There is always a certain amount of personnel that leave an organization...

Problem 8. A hat contains two coins. Coin #1 has P(heads) = 1/4. Coin #2 has P(heads) = 3/4. A coin is selected at random from the hat and tossed 4 times. (The same coin is tossed four times.) (a) If...

Because of staffing decisions, managers of the Gibson-Marimont Hotel are interested in the variability in the number of rooms occupied per day during a particular season of the year. A sample of 20...

Choose one of your favorite or most frequented retailers. Do you feel more motivated to spend money when you shop at their in store location or online location and explain why? Why do you prefer to...

You just took out a loan for $ 6 6 , 5 5 5 that requires X monthly payments of $ 1 , 2 1 0 . The interest rate on the loan is 0 . 5 7 percent per month and the first regular payment will be made...

15-18. Access the Web site of an ERP vendor such as Oracle, SAP, Infors, i2 Technologies or QAD. Make a list of the modules available. Choose one module to describe in detail.

A snack company packages and sells three different 1-pound canned party mixes: Plain Nuts, Mixed Nuts, and Premium Mix. Plain Nuts sell for $2.25 per can, Mixed Nuts sell for $3.37, and Premium Nuts...

An investor is considering three different television news stocks to complement his portfolio: British Broadcasting Company (BBC), Canadian Broad-casting Company (CBC), and Australian Broadcasting...

The mathematical relationships that follow were formulated by an operations research analyst at the Smith-Lawton Chemical Company. Which ones are invalid for use in an LP problem? Why? Maximize...

How do you calculate the expected value for this goodness of fit test? The Frequency is the observed value how do you compute the expected value in this problem from that The results of a recent...

Conduct the hypothesis test and provide the test statistic and the critical value, and state the conclusion. A person randomly selected 100 checks and recorded the cents portions of those checks. The...

What's the future value of $250,000 after 3 vears if it earns 26% annuallv? What's the present value of $90,000 to be received in 3 years if the annual interest i What annual interest rate would...