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If the individual’s income is either OA = $30,000 with probability of 0.95 or
OB= $5000,
what is the expected income of this individual?
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- 1. Suppose the prices of used cars in the market are normally distributed with a mean of $15,000 and a standard deviation of $7,5000. What is the probability of selecting a car from this market and its priced above $20,000.The probability distribution for the number of automobiles sold during a day (x) at Bob Iron Motors isas follows. x f(x) 0 0.001 1 0.007 2 0.034 3 0.099 4 0.188 5 6 0.220 7 0.136 8 0.055 9 0.015 10 0.001 17 The probability that 5 automobiles will be sold is,a 0.232b 0.244c 0.257d 0.271If the farmer uses pesticides he expects a crop of 60,000 bushels; if he does not use pesticides he expects a crop of 50,000 bushels. The cost of pesticides is $30,000 and the other costs associated with planting and harvesting the crop total $450,000. The price of corn at harvest time will either be $9.00 with probability of 0.50 or it will be $11.00 with probability 0.50, so if the farmer decides to sell the crop at harvest, the expected price per bushel that he will receive is $10.00. If the farmer decides to sell the crop at harvest, then: a. He should not use pesticides because not using pesticides ensures greater expected profit. b. He should not use pesticides because not using pesticides ensures lower expected profit. c. He should use pesticides because using pesticides ensures greater expected profit. d. He should use pesticides because using pesticides ensures lower expected profit.
- Your company must decide whether to introduce a new product. The sales of the product will be either at a high (success) or low (failure) level. The conditional value for this decision is as follows Decision High Low Introduce $4,000,000 -$2,000,000 Do Not Introduce 0 0 Probability 0.3 0.7 You have the option to conduct a market survey to sharpen you market demand estimate. The survey costs $200,000. The survey provides incomplete information about the sales, with three possible outcomes: (1) predicts high sales, (2) predicts low sales, or (3) inconclusive. Such surveys have in the past provided these results Result High Low Predicts High 0.4 0.1 Inconclusive 0.4 0.5 Predicts Low 0.2 0.4 a) Using expected monetary value, what is your decision? b) What is the expected value of perfect information before taking the survey? c) Draw the complete decision tree, including the survey option. d) What is the…If the farmer uses pesticides he expects a crop of 60,000 bushels; if he does not use pesticides he expects a crop of 55,000 bushels. The cost of pesticides is $20,000 and the other costs associated with planting and harvesting the crop total $450,000. The price of corn at harvest time will either be $10.00 with probability of 0.50 or it will be $12.00 with probability 0.50, so if the farmer decides to sell the crop at harvest, the expected price per bushel that he will receive is $11.00. If the farmer does not use pesticides and decides to sell the crop at harvest, what is his expected revenue? a. $550,000.00 b. $660,000.00 c. $600,000.00 d. $605,000.00Consider a city where everyone commutes to the city center and commuting cost per mile per month is $40. Each household occupies a 1,000-square-foot dwelling and has $7,000 worth of possessions in its dwelling. The probability that any particular household will be burglarized (involving the uninsured loss of all possessions) is 0.10 at the city center and decreases by 0.01 per mile (to 0.09 at one mile, 0.08 at two miles, and so on). The housing price is $1.00 per square foot at the city center. a) Draw the housing-price curve for locations up to five miles from the city center.
- You are at a casino and there are three slot machines you can use to bet on. You must have a return of .5% of higher on what you are betting. Below is the expected returns for each slot machine under various scenarios. What combination of machines do you play to maximize your average return? Decision Variables Data Slot 1 100.0% Monday Tuesday Wednesda Average Slot 2 0.0% Slot #1 8% 4% 5% 5.667% Slot 3 0.0% Slot #2 2% -3% 3% 0.667% Slot #3 6% -2% 4% 2.667% Objective 5.7% Constraints 0.08 >= 0.5% 0.04 >= 0.5% 0.05 >= 0.5% 100.0% .: 100%Assume that 5% of the people who receive Treatment A die. The sixty percent who fully recover live another 10 years. The treatment is only partially successful for 35% of the patients, who live another 4 years. What is the expected value of Treatment A, expressed as additional years of life?‘Lottery A’ refers to a lottery ticket that pays $2,000 with a probability of 0.3, $8,000 with a probability of 0.4, $12,000 with a probability of 0.2, and $18,000 with a probability of 0.1.What is the expected value of Lottery A?A) $7200B) $8000C) $9000D) $7900E) None of the above
- The demand for a product of Carolina Industries varies greatly from month to month. The probability distribution in the following table, based on the past two years of data, shows the company's monthly demand. Unit Demand Probability 300 400 500 600 0.20 0.30 0.35 0.15 (a) If the company bases monthly orders on the expected value of the monthly demand, what should Carolina's monthly order quantity be for this product? (b) Assume that each unit demanded generates $70 in revenue and that each unit ordered costs $50. How much will the company gain or lose in a month (indoitars) if it places an order based on your answer to part (a) and the actual demand for the item is 300 units?You decide to invest in a portfolio consisting of 21 percent Stock X, 48 percent Stock Y, and the remainder in Stock Z. Based on the following information, what is the standard deviation of your portfolio? State of Economy Normal Boom Probability of State of Economy .84 .16 Return if Stat Stock X Stock Y 10.20% 3.60% 17.50% 25.50%Consider the lottery that assigns a probability T of obtaining a level of consumption CH and a probability 1-T of obtaining a low level of consumption c, with CH > C1. Consider an individual facing such a lottery with utility function u(c) that has the properties that more is better (that is, a strictly positive marginal utility of consumption at all levels of c) and diminishing marginal utility of consumption, u"(c) < 0. As usual, we are using the shorthand u'(c) consumption and u"(c) = " = dư ( to be the second derivative of the utility function (which is also the derivative of the first derivative of the utility function). du(c) for the first derivative of the utility function with respect to dc du(c) dc2 du' (c) dc