Consider the job market signaling game given the figure below. The worker has two types: H and L, and q is the probability associated with type H. The production functions and indifference curves are as shown in the figure. In a pooling Perfect Bayesian Equilibrium of this game, the range of values possible for equilibrium level of education, Epool is (with an appropriate set of beliefs): (a) e1 only. (b) [e1, e3] (c) [e1, e2] (d) [e2, e3].
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Consider the job market signaling game given the figure below. The worker has two types: H and L, and q is the probability associated with type H. The production
(a) e1 only.
(b) [e1, e3]
(c) [e1, e2]
(d) [e2, e3].
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- 15 For the given Bayesian Game, determine the average payoff for a hardworking (H) teacher for Interested (I) type of students with strategy Not Study (NS) and Not Interested (NI) type of students with strategy Study (S), i.e. Teacher's payoff for strategy (H,(NS,S)). Player-1: Teacher, Player-2: Student Student may be of two categories: INTERESTED (I) or NOT INTERESTED (NH) with probability 1/2. Action of Teacher: Hard work (H/ Laty (L) Action of Student: Study (S)/ Not Study (NS) Game Table: P(I)=1/2 Teacher\ Student NS H. 10,10 0,0 L 5,5 5,0 P(NI)=1/2 Teacher\ Student S NS 5,5 0,5 10,5 5,10Exercise 4. A certain species of plant always has either three or five leaves. The number is random, with P(3 leaves) 0.4 and P(5 leaves) = 0.6. Each plant has a flower which, randomly, is either open or closed, with probabilities P(open) = 0.8 and P(closed) = 0.2. A botanist collects 1000 randomly chosen plants from this species and nds the following distribution of traits: open closed N3,closed 3 leaves N3,open 5 leaves NE,open N5, closed a) Assuming the two traits are independent, determine the expectations of the counts №3,open, N3,closed, N5,0-en, and N5,close in the table. b) Determine an approximate value for the probability P(N3,open > 340). Exercise 5. Assume that we have observed the following values from a normal distribution with known variance o2 = and unknown mean . 1.23 -0.67 1.16 1.67 0.24 2.99 0.02 .17 0.27 21. Test the hypothesis Ho: = 0 against the alternative H₁: #0 at significance level a = 5%. Exercise 6. Let 0> 0 and XU[0,0], i.e. X is uniformly distributed on…3. A construction company submits bids for two projects. Listed in Table 1 are the profit and probability of winning each project. Assume that the outcomes of the two bids are independent. Profit $75,000 Project A Project B $120,000 Chance of Winning Bid 0.50 0.65 Table 1: Projects, Bids, and Profits (a) List the possible outcomes (win/not win) for the two projects and find their probabilities. (b) Let X denote the company's total profit out of the two contracts. Determine the probability distribution of X. (c) If it costs the company $2000 for preparatory surveys and paperwork for the two bids, what is the expected net profit?
- Refer to the contingency table shown below. Smoking by Race for Males Aged 18 to 24 Smoker(S) Nonsmoker(N) Row Total White(W) 290 560 850 Black(B) 30 120 150 Column Total 320 680 1,000 Click here for the Excel Data File (a) Calculate the probabilities given below (Round your answers to 4 decimal places.): Smoking by Race for Males Age 18-24 Smoker Nonsmoker Row Total (S) (N) White (W) 290 560 850 Black (B) 30 120 150 Column Total 320 680 1000 Smoking by Race for Males Age 18-24 Smoker Nonsmoker Row Total (S) (N) White (W) 290 560 850 Black (B) 30 120 150 Column Total 320 680 1000Part II. A medical clinic has collected the following data on patient category and health state of 300 patients. health state Women patient category Men Children Severe 20 30 25 Non-severe 100 75 50 One of these patients is selected at random. Let W= the patient is a woman; M = the patient is a man; C = the patient is a child; S = the patient's health state is severe; and N= the patient's health state is non-severe. 1. Find P(S n W). Are S and W mutually exclusive? Why 2. Find P(N UC).. 3. Find P(WIN). Are W and N independent? Why? (A payoff table is given as S1 S2 S3 D1 250 750 500 D2 300 -250 1200 D3 500 500 600 a. What choice should be made by the optimistic decision maker? b. What choice should be made by the conservative decision maker? c. What decision should be made under minimax regret? d. If the probabilities of d1, d2, and d3 are .2, .5, and .3 respectively, then what choice should be made under expected value?
- I need help with #3 please.In the strategic form game below: (a.) What is P1's best response to each of P2's strategies. (b.) Find all Pure Strategy Nash Equilibria (PSNE). Show all work. (c.) Show an example of a Mixed Strategy Nash Equilibrium (MSNE) in this game. How many are there? Explain. Hint: we can assign probabilities of 1 or 0 if a player chooses a given strategy with certainty in a MSNE. Show your work. Player 1 a b с d Player 2 W X Y Z 0,5 1,3 1,7 0,8 1,6 0, 2 2,6 0,7 0,5 1,3 0,8 3,9 1,2 0,4 0,4 3,5Let S = {E1, E2, E3} be the sample space of an experiment and let A = {E1}, B = {E2}, and C = events from S. The probabilities of the sample points are assigned as follows: P(E,) = 0.35, P(E2) = 0.30, and P(E3) = 0.35. Find P(BC). {E2, E3} be Select one: O a. 0.65 O b. 0.70 O c. 0.35 O d. 0.30
- Bakery Products is considering the introduction of a new line of products. In order to produce the new line, the bakery is considering either a major or minor renovation of the current plant. Bakery Products has the option of not developing the new line at all. The decision alternatives are shown in the payoff table below as well as the states of nature and probabilities. Payoffs are profits; States of Nature with Profits ($) Decision Alternatives Favourable (F) Neutral Market (U) Unfavourable (U) Major Renovation Minor Renovation $10,000 $5,000 $0 $4,000 $2,000 $0 - $9,000 - $2,000 $0 Do Nothing Probability 0.3 0.4 0.3 Before making the final decision, Bakery Products can pay a market research firm $500.00 to survey consumer attitudes towards the company's products. The results can be either “vibrant" or “limp". The reliability of the company, based on past performance, is given below. Conditional Probability For A Given state of nature Survey Results Vibrant (V) Limp (L) Favourable…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…A study conducted by the Urban Energy Commission in a large metropolitan area indicates the probabilities that homeowners within the area will use certain heating fuels or solar energy during the next 10 years as the major source of heat for their homes. The following transition matrix represents the transition probabilities from one state to another. Electricity 10.2 Natural Gas Fuel Oil Solar Energy Elec. Gas Oil 0.60 0.05 0.10 0.15 0.85 0.10 0.08 Solar 0 0.10 0.02 0.75 0.08 0.15 0.08 0.05 0.84 Among homeowners within the area, 20% currently use electricity, 35% use natural gas, 40% use oil, and 5% use solar energy as the major source of heat for their homes. In the long run, percentage of homeowners within the area will be using solar energy as their major source of heating fuel? (Round your answer to one decimal place. Assume the trend continues.) X % what