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Five of ten people earn $0, four earn $100, and one loses $100. What is the expected payoff? What is the variance of the payoff?
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- A wheel of fortune in a gambling casino has 54 different slots in which the wheel pointer can stop. Four of the 54 slots contain the number 9. For a 1 dollar bet on hitting a 9, if he or she succeeds, the gambler wins 10 dollars plus the return of the 1 dollar bet. What is the expected value of this gambling game? What is the meaning of the expected value result?In a game, there are three values 1, 000, 2.500 and 5,000 and the cost of the game is 1, 500 . If each outcome has an equal probability of occurring, then what is the expected value of playing the game?A wheel of fortune in a gambling casino has 54 different slots in which the wheel pointer can stop. Four of the 54 slots contain the number 9. For $3 bet on hitting a 9, if he or she succeeds, the gambler wins $16 plus return of the $3 bet. What is the expected value of this gambling game? (Present your answer in dollars with 2 decimal places but without $ sign)
- suppose you pay 25 dollars to enter into a raffle with a 400 dollar prize. if you have a 5% chance of winning, the expected value of winning is?a. Mayers & Smith Corp. has a fertilizer plant. The probability of an explosion at the plant depends on how much the firm spends on safety as given by the table below. If an explosion occurs, the loss to society (damaged equipment, death of employees, etc.) is expected to be $250 million. Safety Expenditure $ millions) 0.0 0.5 1.0 1.5 2.0 2.5 Probability of Loss 0.030 0.020 0.016 0.013 0.011 0.010 Find the optimal level of safety from a societal perspective correct calculation of marginal cost and marginal benefit;: correct optimal amount.You have a 50 percent chance of making $0, a 40 percent chance of making $100, and a 10 percent chance of losing $100. Calculate the expected value and variance of the payoff.
- In a final round of a MegaMillion TV show, a contestant has won $1 millionand has a chance of doubling the reward. If he loses his winnings drop to$500,000. The contestant thinks his chances of winning are 50%. Should heplay? What is the lowest probability of a correct guess that will make his betprofitable? Show workConsider an investment that pays off $700 or $1,600 per $1,000 invested with equal probability. Suppose you have $1,000 but are willing to borrow to increase your expected return. What would happen to the expected value and standard deviation of the investment if you borrowed an additional $1,000 and invested a total of $2,000? What if you borrowed $2,000 to invest a total of $3,000? Instructions: Fill in the table below to answer the questions above. Enter your responses as whole numbers and enter percentage values as percentages not decimals (.e., 20% not 0.20). Enter a negative sign (-) to indicate a negative number if necessary. Invest $1,000 Invest $2,000 Invest $3,000 Expected Value Percent Increase Standard Deviation 1150 S 28 % $ 8 % $ Expected Return N/A Doubled Tripled : #The prizes that can be one and a sweepstakes are listed below together with the chances of winning each one: $5900(1 chance in 8600); $2700(1 chance in 5000);$600(1 chance in 4800);$200(1chance in 2500). Find the expected value of the amount won for one entry if the cost of entering is 52 cents
- You take a position with a large real estate development company as your first job after graduation. Your first big assignment is to sell an office building – you have been informed the company’s cost into the building (and the bottom line price it is willing to accept) is $400,000. You have identified a likely buyer and you assess that his top price is either $500,000 with a probability of .3, $600,000 with a probability of .5, or $1,000,000 with a probability of .2. You have to commit to a posted price – what price will maximize your profitability?Suppose that you graduate from college next year and you have two career options: 1) You will start a job in an investment bank paying a $100,000 annual salary. 2) You will start a Ph.D. in economics and, as a student, you will receive a $20,000 salary. You are bad with decisions, so you are letting a friend of yours decide for you by flipping a coin. The probabilities of options 1 and 2 are, therefore, each 50%. a) Illustrate, using indifference curves, your preferences regarding consumption choices in the two different states of the world. Assume that you are risk-averse. [Include also the 45 degrees line in your figure] b) Now show how the indifference curves would change if you were substantially more risk averse than before. Explain. c) Now show the indifference curves if you are risk neutral and if you are risk loving. d) Show your expected utility preferences from point a) mathematically.You have determined that your risk tolerance is 60. Calculate your utility for the following payoffs: (Round your answers to 2 decimal places.) Payoff Utility 8 15 20