Question: A coin (not necessarily fair) will be tossed once, and you have to predict the outcome. If you predict the outcome correctly you win $1000.

A coin (not necessarily fair) will be tossed once, and you have to predict the outcome. If you predict the outcome correctly you win $1000. Otherwise, you lose $5.
(a) What are the states of nature? What is the decision space? Write the utility table.
(b) Suppose that you believe that the probability of heads is 2/3. What is your price for the states of nature? Find the expected gains.
(c) Suppose that you are allowed to toss the coin twice and you find that the first toss results in heads and the second in tails.What are the observables?
(d) Assume the situation in (c). The coin is going to be tossed again and you have to predict the outcome. What is your updated prior?
(e) What are your expected gains, and what is your decision for the situation in (d)?

Step by Step Solution

★★★★★

3.47 Rating (173 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a States of Nature Decision Space Head H Tail T Predicting Head 1000Correct prediction 5 ... 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)

610-M-S-Q-C-B-S (534).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Suppose we have a coin (not necessarily balanced) with p being the probability of heads. Assume a uniform prior for p. Suppose in 20 tosses of this coin, we obtained 12 heads. Obtain a 90% credible...

Suppose we have a coin (not necessarily balanced) with p being the probability of heads. Assume a uniform prior for p. Suppose in 20 tosses of this coin, we obtained 12 heads. Test the hypothesis H0:...

A version of simple exponential smoothing can be used to predict the outcome of sporting events. To illustrate, consider pro football. Assume for simplicity that all games are played on a neutral...

Algorithms in Artificial Intelligence (or, the old name: Introduction to Algorithmic Decision Making) Part 1 Based on slides by David Sarne and Lirong Xia Course Tentative Schedule Introduction...

Probability Ratios: Between 0 and 1 Name Date PROBABILITY RATIOS: BETWEEN 0 AND 1 It is important to point out that in determining the probability of an event, the probability ratio (proper fraction)...

This is lab activity 9, "Simulation and the law of large numbers Select the best answer for each question. An answer may be used once, more than once or not at all. v What does the horizontal line...

Statistics Quiz 6 version 1 name: 1. Use the normal distribution to approximate the desired probability. A certain question on a test is answered correctly by 25.0 percent of the respondents....

After reviewing the attached article. In 350 words explain why do Hard Nosed Executives need theory? because unless the phenomenon is carefully observed and described in its breadth and complexity,...

(20 points) Clarice is an expected utility maximizer and her utility function over money is given by u = x 1 2 . Clarice's friend, Hannibal, has offered to bet with her $1,000 on the outcome of the...

Chapter Six Union Organizing Campaigns This chapter is the first of two chapters that examine how unions organize new bargaining units and how and why employers attempt to avoid being unionized....

What combination of ester and Grignard reagent could you use to prepare each of the following tertiary alcohols?

What personal planning areas and task management skills you can develop and/or improve in Capsim Business simulations?

The largest mutual fund, as of October 2 0 2 1 , held approximately _ _ _ _ _ _ _ _ _ blank billion in assets under management.

Based on Table 10-1, discuss five approaches to assist a firm that desires to make the transition from a full-service provider to a partial or self-service operation.

Solve the inequality In (x2 2x 2

Use indirect reasoning to prove that log2 5is an irrational number.

A driver sets out on a journey. For the first half of the distance she drives at the leisurely pace of 30 mi/h; she drives the second half at 60 mi/h. What is her average speed on this trip?

i need help with this question 1. Which statement cannot be justified by one of the properties of real numbers? A. (a + b) + c = a+ (b+c) B. a - (b + c) = (a -b) + c C. (ab)c = a(bc) D. (a + b) + 0=...

Analyzing Manufacturing Cost Accounts Clapton Company manufactures custom guitars in a wide variety of styles. The following incomplete ledger accounts refer to transactions that are summarized for...

Gregor Mendel published his results from his experiments on simultaneous inheritance of pea plant phenotypes in 1866 (Mendel, 1866). He examined 556 plants and classi?ed them according to their form...