Required information An officer of the state lottery commission has sampled lottery ticket purchasers over a 1-week period at one location. The amounts distributed back to the purchasers and the associated probabilities for 5000 tickets are as follows: 2 5 10 Distribution, $ 0 Probability 0.91 0.045 0.025 0.013 NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. 100 0.007 If tickets cost $2, determine the expected long-term income to the state per ticket, based on this sample. The expected long-term income to the state is 96 cents per ticket.
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- Explain probability and nonprobability samplingtechniques.A company is developing a new cell phone and has two models under consideration, Model 1 and Model 2. Market research indicates that 70% of the new phone have a high consumer demand and 30% have a 30% low consumer demand. Model 1 Model 2 Investment Required $ 200,000 $ 175,000 Revenue for High Demand $ 500,000 $ 160,000 Revenue for Low Demand $ 450,000 $ 160,000 Develop a decision tree to find the best modelKier, the industry analyst of Globe, wants to determine the propensity of Major Internet companies toward risk. He was able to determine the utility distribution of Globe, PLDT and Converge. For Globe, If the expected payoff of a venture is a loss of 50,000, the utility value is 0.00, if a loss of 25,000, the utility value is .2, if breakeven, the utility value is .5, if gain of 25,000 .8 and if gain of 50,000 utility value is 1. For PLDT, if loss of 50,000 utility value is 0, if loss of 25,000 utility value is .1, breakeven is .4, if a gain of 25,000, utility value is .7 and if gain of 50,000 utility value is 1. For Converge, if loss of 50,000, utility value is 0, if loss of 25,000, utility value is .3 breakeven is .6, if gain of 25,000, utility value is .9 and gain of 50,000, utility value is 1. What is the propensity to risk of the three internet companies? Explain your graph.
- 1. Individual Problems 18-1 You hold an oral, or English, auction among three bidders. You estimate that each bidder has a value of either $88 or $110 for the item, and you attach probabilities to each value of 50%. The winning bidder must pay a price equal to the second highest bid. The following table lists the eight possible combinations for bidder values. Each combination is equally likely to occur. On the following table, indicate the price paid by the winning bidder. Combination Number Bidder 1 Value Bidder 2 Value Bidder 3 Value Probability Price ($) ($) ($) 1 $88 $88 $88 0.125 2 $88 $88 $110 0.125 3 $88 $110 $88 0.125 4 $88 $110 $110 0.125 5 $110 $88 $88 0.125 6 $110 $88 $110 0.125 7 $110 $110 $88 0.125 8 $110 $110 $110 0.125 The expected price paid is . Suppose that bidders 1 and 2 collude and would be willing to bid up to a maximum of their values, but the two bidders…The Gorman Manufacturing Company must decide whether to manufacture a component part at its Milan, Michigan, plant or purchase the component part from a supplier. The resulting profit is dependent upon the demand for the product. The following payoff table shows the projected profit (in thousands of dollars): state of nature low demand medium demnad high demand Decision alternative s1 s2 s3 manufacture d1 -20 40 100 purchase d2 10 45 70 The state-of-nature probabilities are P(s1) = 0.35, P(s2) = 0.35, and P(s3) = 0.30. a. Use expected value to recommend a decision. b. Use EVPI to determine whether Gorman should attempt to obtain a better estimate of demand.The Gorman Manufacturing Company must decide whether to manufacture a component part at its Milan, Michigan, plant or purchase the component part from a supplier. The resulting profit is dependent upon the demand for the product. The following payoff table shows the projected profit (in thousands of dollars): state of nature low demand medium demnad high demand Decision alternative s1 s2 s3 manufacture d1 -20 40 100 purchase d2 10 45 70 The state-of-nature probabilities are P(s1) = 0.35, P(s2) = 0.35, and P(s3) = 0.30. a. A test market study of the potential demand for the product is expected to report either a favourable (F) or unfavourable (U) condition. The relevant conditional probabilities are as follows: P(F|S1)=0.10 P (U|S1)=0.90 P(F|S2)=0.40 P (U|S2)=0.60 P(F|S3)=0.60 P (U|S3)=0.40 A.Compute the probabilities by completing the table Sate of…
- The Gorman Manufacturing Company must decide whether to manufacture a component part at its Milan, Michigan, plant or purchase the component part from a supplier. The resulting profit is dependent upon the demand for the product. The following payoff table shows the projected profit (in thousands of dollars): state of nature low demand medium demnad high demand Decision alternative s1 s2 s3 manufacture d1 -20 40 100 purchase d2 10 45 70 The state-of-nature probabilities are P(s1) = 0.35, P(s2) = 0.35, and P(s3) = 0.30. a. A test market study of the potential demand for the product is expected to report either a favourable (F) or unfavourable (U) condition. The relevant conditional probabilities are as follows: P(F|S1)=0.10 P (U|S1)=0.90 P(F|S2)=0.40 P (U|S2)=0.60 P(F|S3)=0.60 P (U|S3)=0.40 What is the expected value of the market research information?…The Gorman Manufacturing Company must decide whether to manufacture a component part at its Milan, Michigan, plant or purchase the component part from a supplier. The resulting profit is dependent upon the demand for the product. The following payoff table shows the projected profit (in thousands of dollars): state of nature low demand medium demnad high demand Decision alternative s1 s2 s3 manufacture d1 -20 40 100 purchase d2 10 45 70 The state-of-nature probabilities are P(s1) = 0.35, P(s2) = 0.35, and P(s3) = 0.30. a. A test market study of the potential demand for the product is expected to report either a favourable (F) or unfavourable (U) condition. The relevant conditional probabilities are as follows: P(F|S1)=0.10 P (U|S1)=0.90 P(F|S2)=0.40 P (U|S2)=0.60 P(F|S3)=0.60 P (U|S3)=0.40 A.Compute the probabilities by completing the table Sate of…Question 2An investor is to purchase one of three types of real estate, as illustrated inFigure below. The investor must decide among an apartment building, anoffice building, and a warehouse. The future states of nature that willdetermine how much profit the investor will make are good economicconditions and poor economic conditions. The profits that will result fromeach decision in the event of each state of nature are shown in Table below: Assume that it is now possible to estimate a probability of 0.60 that goodeconomic conditions will exist and a probability of .40 that poor economicconditions will exist. a) Determine the best decision by using expected opportunity loss. b) Develop a decision tree, with expected values at the probability nodes. c) Compute the expected value of perfect information.
- A new product has the following profit projections and associated probabilities: Profit Probability $150,000 0.10 $100,000 0.25 $ 50,000 0.20 $0 0.15 -$ 50,000 0.20 -$100,000 0.10 Use the expected value approach to decide whether to market the new product. 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? Assume that the following indifference probabilities are assigned. Do the utilities reflect the behavior of a risk taker or a risk avoider? Profit Indifference Probability $100,000 0.95 $ 50,000 0.70 $0 0.50 -$ 50,000 0.25Given ten historical returns: [-15%, -13%, -10%, -5%, -3%, 1%, 4%, 7%, 11%, 20%], what is the 20% conditional value at risk (CVaR) under the empirical distribution? Select one: a. -15% b. -14% c. -13% d. -10% e. 11%I am in possession of two coins. One is fair so that it lands heads (H) and tails (T)with equal probability while the other coin is weighted so that it always lands H. Bothcoins are magical: if either is flipped and lands H then a $1 bill appears in your wallet,but when it lands T nothing happens. You may only flip a coin once per period. Theinterest rate is i per period. You are risk-neutral and thus only concern yourself withexpected values (and not variance). For simplicity, in the questions below assumeyou will live forever.1. How much are you willing to pay for such a coin that you know is fair? 2. How much are you willing to pay for such a coin that you know is weighted? 3. I currently own the coins and know which is fair and which is weighted, but youcannot tell which is which. You may make an offer to purchase a coin of yourchoosing, which I am free to accept or reject. What is the most you are willingto offer? Explain how you arrived at this answer.