The following payoff table shows profits associated with a set of 3 alternatives under 2 possible states of nature. If the probability of S1 is 0.5, what is the optimal alternative using the expected value approach? State of Nature OY Z X Alternatives X Y Z 12 -28 4 10 5 Cannot be determined.
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- i need detailed solutionThe following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature. Decision Alternative = States of Nature 51 52 53 d₁ d₂ Suppose that the decision maker obtained the probabilities P(s₁) = 0.65, P(5₂) = 0.15, and P(53) = 0.20. Use the expected value approach to determine the optimal decision. EV(d₁) EV(d₂) = The optimal decision is? . 240 90 90 15 90 65In the following profit payoff table for a decis problem with two states of nature and three alternatives, the prior probabilities for s1 and P(81) = .8 and P(82) = .2. Excel File: data20-15.xls State of Nature Decision Alternative $2 d, dz dz 15 10 12 20 10 a. What is the optimal decision? - Select your answer - b. Find the EVPI. c. Suppose that sample information I is obta with P(I|81) = .20 and P(I|82) = .75. Find the posterior probabilities P(81|1) and P(s; decimals). P(81|I) = P(82\I) =
- A decision maker faced with four decision altematives and four states of nature develops the following profit payoff table. States of Nature Decision Alternative s. 52 5 5. d. 12 7 3 5 d, 7 d. 6 8 9 11 The decision maker obtains information that enables the following probabilities assessments: P(s,) = 0.5, P(s,) = 0.2, P(s,) = 0.2, and P(s,) = 0.1. (a) Use the expected value approach to determine the optimal decision. EV(d,) EV(d,) EV(d,) EV(d.) The optimal decision is (b) Now assume that the entries in the payoff table are costs. Use the expected value approach to determine the optimal decision. The optimal decision is ? v inA cellphone provider has the business objective of wanting to determine the proportion of subscribers who would upgrade to a new cellphone with improved features if it were made available at a substantially reduced cost. Data are collected from a random sample of 600 subscribers. The results indicate that 131 of the subscribers would upgrade to a new cellphone at a reduced cost. Reducing the price will be profitable if at least 20% of the subscribers would upgrade. Complete parts (a) and (b) below. Question content area bottom Part 1 a. At the 0.01 level of significance, is there evidence that more than 20% of the customers would upgrade to a new cellphone at a reduced cost? Determine the null hypothesis, H0, and the alternative hypothesis, H1. A. H0: π=0.20 H1: π≠0.20 B. H0: π≥0.20 H1: π<0.20 C. H0: π≤0.20 H1: π>0.20 D. H0: π≠0.20 H1: π=A company is facing three types of decisions for the purchasing of a seasonal product. The profitprojection may depend on the demand level. The payoffs for the situations are given in the followingtable:DemandDecision High (s1) Medium (s2) Low (s3)d1 60 60 50d2 80 80 30d3 100 70 101. If the prior probabilities are 0.3, 0.3, and 0.4, respectively, what is the recommended decision?Show all the calculations and answer with a decision tree.2. At each preseason sales meeting, the vice president of sales provides a personal opinion regarding potential demand for the product. The prediction of the vice president have alwaysbeen either excellent (E) or very good (G). Posterior probabilities are as follows.P(V)=0.7; P(E)=0.3P(s1|E)=0.34; P(s1|V)=0.2P(s2|E)=0.32; P(s2|V)=0.26;Use a decision tree to give the optimal decision strategy.43. Give the EVPI and the EOL, and EVSI.4. Suppose that the prior probability of a low demand is always fixed to 0.4, give a sensitivityanalysis on the other…
- Will improving customer service result in higher stock prices for the companies providing the better service? "When a company's satisfaction score has improved over the prior year's results and is above the national average (currently 75.7), studies show its shares have a good chance of outperforming the broad stock market in the long run." The following satisfaction scores of three companies for the 4th quarters of two previous years were obtained from the American Customer Satisfaction Index. Assume that the scores are based on a poll of 67 customers from each company. Because the polling has been done for several years, the standard deviation can be assumed to equal 6 points in each case. Company Year 1 Score Year 2 Score Rite Aid 73 75 Expedia 72 75 J.C. Penney 73 74 a. For Rite Aid, is the increase in the satisfaction score from year 1 to year 2 statistically significant? Use a = .05 and null hypothesis is Ho : H1 – 42 <0. What can you conclude? z value (to 2 decimals) p-value (to…You are considering purchasing stand-alone shares in two companies: Company A and Company B. While both companies expect a rate of return of 15% under normal market conditions, the possible returns under strong and weak economies differ. There is a 30% chance of a weak economy outcome, a 30% chance of a strong economy outcome, and a 40% chance of a normal outcome. For Company A, under a strong economy, they expect a return of 75%. Under a weak economy, they expect a return of -45%. For Company B, under a strong economy, they expect a return of 23%. Under a weak economy, they expect a return of 7.5%. 1. Create a probability distribution table for both companies. 2. Calculate the standard deviation for both companies. 3. With the distribution, create either a bar graph or a bell curve to graph the two companies. 4. From your calculations, describe which company you would consider investing in, if you were risk averse.The following payoff table shows the profit for a decision problem with two states of nature anwo decision alternatives. Decision Alternative d₁ d₂ 052 Submit Answer - [-/6 Points] State of Nature $1 11 5 (a) Suppose P(s) = 0.2 and P(s₂) = 0.8. What is the best decision using the expected value approach? The best decision is --?--✓ with an expected value of DETAILS $2 (b) Perform sensitivity analysis on the payoffs for decision alternative d₁. Assume the probabilities are as given in part (a), an solution found in part (a) optimal. 2 As long as the payoff for s, under d, is |--?-- ▼ 1 4 As long as the payoff for s, under d₁ is --?-- v 2 Is the solution more sensitive to the payoff under state of nature s₁ or s₂? O 51 then the solution found in part (a) will be optimal. then the solution found in part (a) will be optimal. CAMMIMS16 14.E.015.
- Consider the following game in a game arcade. The probability of winning a game is p and hence loosingthe game is 1 − p. In order to win a prize you are given three choices:• A: win at least once in 6 games;• B: win at least twice in 12 games; and• C: win at least 3 times in 18 games.1. If p = 16 which of A, B, or C should you choose to maximize your probability of winning the prize?You are required to compute the probabilities for each option to justify your answer.2. Using the formulas derived in part (1), write a R-code to compute (not simulate) and plot the probabilityof winning the prize for options A, B, and C for different values of p varying from 0.1 to 0.9 inincrements of 0.1. Summarize your observation.Regarding the plot: i) All three curves should be drawn in the same plot, ii) Make sure that the threecurves are distinguishable (using different line styles, colors, and/or markers), and iii) make sure toadd a legend that identifies the curves for the three different options…Suppose that you are given a decision situation with three possible states of nature: S₁, S₂, and s3. The prior probabilities are P(s₁) = 0.3, P(s₂) = 0.2, and P(S3) = 0.5. With sample information I, P(I|s₁) = 0.1, P(I|s₂) = 0.05, and P(I|s3) = 0.2. Compute the revised or posterior probabilities: P(S₁|I), P(S₂|I), and P(S3I). (Round your answers to four decimal places.) P(S₁|I) P(S₂|I) P(S3|1)
