B. Following table gives Payoffs for actions A1, A, and A; corresponding to states ofnature S, and S, whose chances are 0-6 and 0-4 respectively.States of NatureActionsA,A3S,162018S,191512Find decisions under:(i) Maximin criterion(ii) EMV criterion.

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Answered: 8. Following table gives Payoffs for…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The 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 65
2. In a market in which the Arbitrage Pricing Theory (APT) model holds, the expected return is given by E[R] = 20 +ẞi,₁₁ + Bizd₂+, ..., +ßi,nan a) Assume that risk-free rate in this economy is 0.02. Consider a two-factor model, n = 2 and two well diversified portfolios P₁ and P2 with the following features: Expected returns: E(R₁) Sensitivity to factor 1: ẞi,1 P₁ 0.18 P₂ 0.05 0.2 0.1 0.7 0.3 Sensitivity to factor 2: Biz Find the risk premiums for each factor.
2. In a market in which the Arbitrage Pricing Theory (APT) model holds, the expected return is given by E[R] = 20 + B₁₁₁₁ + Bizd₂+,...,+Binan Assume that risk-free rate in this economy is 0.02. Consider a two-factor model, n = 2 and two well diversified portfolios P₁ and P₂ with the following features: Expected returns: E(R¡) P₁ 0.18 Sensitivity to factor 1: B₁₁ Sensitivity to factor 2: Biz 0.2 0.7 P₂ 0.05 0.1 0.3 b) Assume there is another well diversified security P3 in this economy with factor sensitivities, ẞ3,1 = 0.2, and 3,2 = 0.7. The expected return of this security is E(R3) = 0.25. State whether the APT is satisfied. If yes, explain why, if not propose an arbitrage strategy.
The accompanying data came from a study of collusion in bidding within the construction industry. No. Bidders No. Contracts 2 3 4 5 6 7 8 9 10 11 USE SALT 8 20 26 18 12 8 6 7 4 3 (a) What proportion of the contracts involved at most five bidders? At least five bidders? (Round your answers to four decimal places.) at most five bidders. at least five bidders X X (b) What proportion of the contracts involved between five and 10 bidders, inclusive? Strictly between five and 10 bidders? (Round your answers to four decimal places.) between five and 10 bidders, inclusive strictly between five and 10 bidders X X
H1.
1. Two risk neutral players compete to win a prize, P. The probability of winning depends on effort; the probability that player i wins equals e(e++e2), where ei is the effort level of player i. The cost of effort is ciei. a) Find the Nash equilibrium effort levels. b) What is the probability player 1 wins at equilibrium?
In 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) =
What is the ratio of the total jobs at risk in Transportation and Storage to those at riks in Retail? A) 4.68:7.79 B) 7.79:4.68 C) 52:41 D) 9:19 E) 30:27
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 in
1. A company is contemplating the introduction of a new product with new packing to replace the existing product at much higher Price (P) or a moderate change in the composition of the existing product with a new packaging at a small increase in price (P2) or a small change in the composition of the existing product except the word "new" with a very small increase in price (P3). The three possible states of nature are : (i) high increase in sales (n), (ii) no change in sales (n), and (iii) decrease in sales (na). The marketing department of the company calculated the payoffs in terms of yearly net profits from each of the strategies (expected sales). This is represented in the following table : Strategies States of Nature 3000 1500 PI P2 P3 7000 5000 3000 4500 3000 3000 Which strategy should the concerned executive choose on the basis of: (i) Maximin criterion, (ii) Laplace criterion ?
8. The NACHR ion channel can be in one of three states: resting (R), closed with Ach bound (C), and open (0) with transition probabilities (per one microsecond): 0.04 (from R to C), 0.07 (from C to R), 0.12 (from C to O) and 0.02 (from O to C); the other transition probabilities are 0. Suppose that initially 3/4 of ion channels are in R and 1/4 are in C. What fraction of the ion channels is open after 1 microsecond? After 2 microseconds? 9. There are three kinds of vegetation in an ecosystem: grass, shrubs, and trees. Every year, 25% of grassland plots are converted to shrubs, 20% of shrub plots are converted to trees, 8% of trees are converted to shrubs, and 1% of trees are converted to grass; the other transition probabilities are 0. Suppose that initially the ecosystem is evenly split: 1/3 grass, 1/3 shrubs and 1/3 trees. What fraction of ecosystem is covered in shrubs after 1 year? after 2 years?
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…

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8. Following table gives Payoffs for actions A1, Az and A; corresponding to states of mature S, and S, whose chances are 0-6 and 0-4 respectively. States of Nature Actions A, A2 A3 S, 16 20 18 S, 19 15 12 Find decisions under: (i) Maximin criterion (ii) EMV criterion.