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 10 100 Distribution, $ 0 Probability 5 0.025 0.85 0.105 0.013 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 cents per ticket.
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- Kier, 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.A random variable has a triangular probability density function with a = 50, b = 375, and m = 250. What is the probability that the random variable will assume a value between 60 and 250? If required, round your answer to four decimal places.Given that Z is distributed as a standard normal random variable, what is Pr(Z > -0.04)? Round your answer to three decimal places, e.g. 0.251.
- the following probability distribution represents the number of people living in a household (x), and the probability of occurrence (p(x). compute the expected value (mean), the variance, and standard deviation for the random variable. calculations for the mean.x 1 2 3 4 5p(x) .33 .29 .27 .07 .04Bob is working on two separate probabilityrelated projects. The first involves the variable N, which is the number of consecutively filled bottles of an anticancer drug that weigh in above the weight specification limit. The variable N is described by the formula (0.5)N because each unit has a 50-50 chance of being below or above the limit. The second involves the battery life L, which varies between 2 and 5 months. The probability distribution is triangular with the mode at 5 months, which is the design life. Some batteries fail early, but 2 months is the smallest life experienced thus far. (a) Write out and plot the probability distributions and cumulative distributions for N and L for Bob. (b) Determine P(N = 1, 2, or 3) consecutive units above the weight limitQuestion 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 property owner is faced with a choice of: A large-scale investment to improve her flats. This could produce a substantial pay-off in terms of increased revenue net of costs but will require an investment of 1.4 million pesos. After extensive market research it is considered that there is a 40% chance that a pay-off of 2.5million will be obtained, but there is a 60% chance that it will be only 800,000 pesos. A smaller scale project to re-decorate her premises. At 500,000 pesos this is less costly but will produce a lower pay-off. Research data suggests a 30% chance of a gain of one million pesos but a 70% chance of being only 500,000 pesos. Continuing the present operation without change. It will cost nothing but neither will it produce any pay-off. Clients will be unhappy and it will become harder to rent the flats out when they become free. What is the best alternative? Use decision tree analysis.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 0.25P06_35.xlsx Shoe demand distribution Demand (100s of pairs) Probability 1 0.025 2 0.050 3 0.075 4 0.100 5 0.150 6 0.200 7 0.175 8 0.100 9 0.075 10 0.050 A buyer for a large department store chain must place orders with an athletic shoe manufacturer six months prior to the time the shoes will be sold in the department stores. The buyer must decide on November 1 how many pairs of the manufacturer’s newest model of tennis shoes to order for sale during the coming summer season. Assume that each pair of this new brand of tennis shoes costs the department store chain $65 per pair. Furthermore, assume that each pair of these shoes can then be sold to the chain’s customers for $90 per pair. Any pairs of these shoes remaining unsold at the end of the summer season will be sold in a closeout sale next fall for $20 each. The probability distribution of consumer demand for these tennis shoes during the coming…
- Players would draw a card from a standard 52 card deck. Whatever card they drew determined what they won. If they draw a face card (Jack, King, Queen) then they win $5. If they draw an Ace, they win $15. For all other cards, they win nothing. A. Fill out the probability distribution table with the probabilities of each possible outcome for this game. Round decimals to four places. x $15 $5 $0 P(x) B. What is the expected value of the distribution above? (Round to the nearest cent, two decimal places.) C. If players were charged $2 per game, would they make and average profit on the games over time, or would they take an average loss over time? D. If players were charged $3 per game, would they make and average profit on the games over time, or would they take an average loss over time?The cost C(Q) of producing a quantity Q of widgets to satisfy demand isC(Q) = 4000+20Q, but the quantity demanded is random. If the mean and standarddeviation of demand are 500 and 200, respectively, then what are the mean andstandard deviation of costs?A company that manufactures and sells T-shirts for sporting events, is providing shirts for an upcoming tournament. Each shirt will cost $7 to produce and will be sold for $13. Any unsold shirts at the end of the tournament can be sold for $5 apiece in the near future. The company assumes the demand for the shirts will be 1,500,3,000,4,500, or 6,000. The company also estimates that the probabilities of each of these sales levels occurring will be 20%, 25%,25%, and 30%, respectively. Determine the expected monetary value of the project if the company chooses to print 4,500 shirts for the tournament. The expected monetary value is---- (Type a whole number.)