The pay-offs (in$) of three acts A1,A2 and A3 and the possible states of nature S1 S2 and S3 are given below: State of nature Acts A2 -20 A2 АЗ S1 -50 200 S2 200 -100 -50 s3 400 600 300 The probabilities of the states of nature are 0.3, 0.4 and 0.3 respectively. Determine the optimal act using the expectaton principle.
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- Consider an economy with two states of nature and one time period. An option pays $3 in state 1 and $0 in state 2, and is being traded for the price of $1. A forward contract pays $3 in state 1 and -$2 in state 2. Using this information, compute the risk-free rate and the risk-neutral probabilities for each state of nature.3. Using the following table, perform ALL FIVE of the techniques for Decision Making under Uncertainty: Maximax, Maximin, Hurwicz Realism (α = 0.4), LaPlace and Minimax Regret. You must show your work for obtaining the points. SIZE OF FIRST STATION GOOD MARKET FAIR MARKET POOR MARKET ($) ($) ($) Small 50,000 20,000 -10,000 Medium 80,000 30,000 -20,000 Large 100,000 30,000 -40,000 Very large 300,000 25,000 -160,0003. Using the following table, perform ALL FIVE of the techniques for Decision Making under Uncertainty: Maximax, Maximin, Hurwicz Realism (α = 0.4), LaPlace and Minimax Regret. You must show your Work in a SINGLE Excel file. SIZE OF FIRST STATION GOOD MARKET FAIR MARKET POOR MARKET ($) ($) ($) Small 50,000 20,000 -10,000 Medium 80,000 30,000 -20,000 Large 100,000 30,000 -40,000 Very large 300,000 25,000 -160,000
- 32. A hardware company sells a lot of low-cost, highvolume products. For one such product, it is equallylikely that annual unit sales will be low or high. Ifsales are low (30,000), the company can sell theproduct for $20 per unit. If sales are high (70,000),a competitor will enter and the company will be ableto sell the product for only $15 per unit. The variablecost per unit has a 20% chance of being $10, a 60%chance of being $11, and a 20% chance of being $12.Annual fixed costs are $20,000.a. Use simulation to estimate the company’s expectedannual profit.b. Find a 95% interval for the company’s annualprofit, that is, an interval such that about 95% ofthe actual profits are inside it.c. Now suppose that annual unit sales, variable cost,and unit price are equal to their respective expectedvalues—that is, there is no uncertainty. Determinethe company’s annual profit for this scenario.d. Can you conclude from the results in parts a and cthat the expected profit from a simulation is…Consider a first-price sealed bid auction of a single object with two bidders j = 1,2 and no reserved price. Bidder 1's valuation is v1 = 2. and bidder 2's valuation is v2= 5. Both v1 and v2 are known to both bidders. Bids must be in whole dollar amounts. In the event of a tie, the object is awarded by a flip of a fair coin. Is there a Nash equilibrium? What is it? Is it unique? Is it efficient?If the decision maker knows nothing about the probabilities of the four states of nature, what is the recommended decision using MAXIMAX CRITERION? D1 D2 D3 D4 What decision alternative will he choose if using MAXIMIN CRITERION? D1 D2 D3 D4 What about MINIMAX REGRET CRITERION? D1 D2 D3 D4 What decision would he make if using criterion of realism at alpha 0.6 is used? D1 D2 D3 D4
- In the study of evolutionary behavior, the Trivers-Willard hypothesis indicates that healthyparents should tend to have more male offspring than female, and that weaker parents should tendto have more female offspring than male. This tendency may maximize the number of each parent’sgrandchildren (and thus help to ensure that its genetic code is preserved) since a healthy maleoffspring can win many mates, but a relatively unhealthy offspring has the best chance of mating ifit is female. In an experiment to examine this hypothesis, a group of 40 opossums were monitoredand 20 of them were given an enhanced diet. After a certain period of time, the opossums with theenhanced diet had raised 19 male offspring and 14 female offspring, and the opossums without theenhanced diet had raised 15 male offspring and 15 female offspring. Does this finding provideevidence in support of the Trivers-Willard hypothesis? (a) Describe the unknown parameters ?1 and ?2. Then state the null and…Suppose two forces Red and Blue, with Red having a starting force = 2, and Blue having a starting force = 1. Engage in a stochastic Lanchester battle assuming square law, in a fight-to-the-finish, with Red a = 0.01 casualties per minute, and Blue b = 0.03 casualties per minute. (a) What is the expected time of the first casualty?(b) What is the probability that there are no casualties in the first 20 minutes?(c) What is the expected number of Red survivors and the expected length of the battle?Hypertension A national study found that treating people appropriately for high blood pressure reduced their overall mortality by 20%. Treating people adequately for hypertension has been dif- ficult because it is estimated that 50% of hypertensives do not know they have high blood pressure, 50% of those who do know are inadequately treated by their physicians, and 50% who are appropriately treated fail to follow this treat- ment by taking the right number of pills. 1 If the preceding 50% rates were each reduced to 40% by a massive education program, then what effect would this change have on the overall mortality rate among true hypertensives; that is, would the mortality rate decrease and, if so, what percentage of deaths among hypertensives could be prevented by the education program?
- A dealer wishes to purchase a number of fans and sewing machines. He has only 5760 ETB to invest and has space for almost 20 items. A fan costs him 360 ETB and sewing machine 240 ETB. His expectation is that he can sell a fan at profit of 22 ETB and a sewing machine at a profit of 18 ETB. Assuming that he can sell all the items that he can buy, how should he invest his money in order to maximize his profit? (Note: ETB = Ethiopian Birr) Formulate it as a linear programming problem (LPP) Use the graphical method to solve it.Given three independent Bernoulli processes Xn, Yn, Zn with success probabilities given as 0.10, 0.87, and 0.26, respectively. X and Y are merged into one Bernoulli process which is merged with Z after. Find the resulting success probability of the last Bernoulli process. (Note: the answer should be in 4 decimal points)Of all customers purchasing automatic garage-door openers,75% purchase a chain-driven model. Let X 5 thenumber among the next 15 purchasers who select thechain-driven model.a. What is the pmf of X?b. Compute P(X . 10).c. Compute P(6 # X # 10).d. Compute m and s2.e. If the store currently has in stock 10 chain-drivenmodels and 8 shaft-driven models, what is the probabilitythat the requests of these 15 customers can allbe met from existing stock?