Two investment options exhibit the following range of outcomes, depending on the state of the economy: State Option 1 Option 2 200 Boom 900 Normal 300 400 Recession -900 -200 The chances that the economy will boom, be normal, and contract are, respectively, 30% (boom), 40% (normal), and 30% (recession). If the decision maker is risk- averse, which of the following statements is true? O The expected value is higher for Option 1, and variance is higher for Option 1 as well. Therefore, a risk-averse decision maker prefers to invest in Option 1. O The expected value is higher for Option 1, but variance is higher for Option 2. It is not clear whether a risk-averse decision maker prefers to invest in Option 1 or Option 2. O The expected value is higher for Option 2, and variance is higher for Option 2 as well. It is not clear whether a risk-averse decision maker prefers to invest in Option 1 or Option 2. O The expected value is higher for Option 2, and variance is higher for Option 1. Therefore, a risk-averse decision maker prefers to invest in Option 2.

An actuary is analyzing the lapse experience of his company's whole life product. The tabulated results are as follows: Age group % of whole life policyholders probability of lapsing 8 % < 20 5 % 20 – 29 13 % 5 % 30 – 39 21 % 4 % 40 – 49 29 % 4 % 50 – 59 17 % 3 % 60 + 12 % 2 % Since the age group 40-49 is the most profitable, what is the probability that a lapsed policy will belong to this cohort?

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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?

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…

You have done risk analysis and determine the following risks and their probabilities could affect your project. Based on these risks, what should you contingency reserve be? Risk 1: 50% chance of a weather delay costing $5,000Risk 2: 20% chance of a worker strike costing $10,000Risk 3: 10% chance of catastrophic failure costing $50,000

An investor has a certain amount of money available to invest now. Three alternative investments are available. The estimated profits, in Kwacha, of each investment under each economic condition are indicated in the following payoff table:   Event Investment selection A B C Economy declines 500 -2000 -7000 No charge 1000 2000 -1000 Economy Expand 2000 5000 20,000   Based on his own past experience, the investor assigns the following probabilities to each economic condition: P (Economy declines) = 30      P (No Change) = 0.50    P (Economy expands) = 0.20 Determine the optimal action based on the maximax criterion Determine the optimal action based on the maximin criterion iii. Compute the expected monetary value (EMV) for each investment

A new product has the following profit projections and associated probabilities: Profit                               Probability  $150,000                          .10 $100,000                          .25 $50,000                            .20 $0                                     .15 -$50,00                             .20 -$100,000                         .10 a) use the expected value approach to decide whether to market the new product b) because of the high dollar values involved, especially the possibility of a $100,000 loss, the marketing vice president has expressed some concern about the use of the expected value approach. As a consequence, if a utility analysis is performed, what is the appropriate lottery? c) assume that the following indifference probabilities are assigned.  Profit                        indifference Probability (p) $100,000                                .95 $50,000                                  .70 $0                                           .50…