Suppose Var(X) = 88, Var(Y) = 82, and X and Y are independent. What is Var(.36X + .64Y)? Suppose Var(X) = 26, Var(Y) = 74, and X and Y are independent. What is Var(.36X + .64Y)?
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- n people guess an integer between 1 and 100, and the winner is the player whose guess is closest to the mean of the guesses + 1 (ties broken randomly). Which of the following is an equilibrium: a) All announce 1. b) All announce 50. c) All announce 75. d) All announce 100State the Gauss-Markov Theorem.Four apples and four oranges are distributed between two boxes in such a way that each of them has four fruits. At each step, we withdraw one fruit from each box and exchange them. Let Xn be the number of apples in the first box. Give the transition probability matrix for Xn. Find long run proportion which is to find Pi1,Pi2,Pi3,Pi4.
- Suppose that Var(X) = 661.1, Var(X) = 8021.53, and Cov(X,Y) = 1922.11. What is Var(.64X + .36Y)? Suppose that Var(X) = 869.03, Var(X) = 7850.84, and Cov(X,Y) = 2238.69. What is Var(.67X + .33Y)?In the Markowitz portfolio optimization model defined in equations (8.10) through (8.19) in the text, the decision variables represent the percentage of the portfolio invested in each of the mutual funds. For example, FS = 0.25 in the solution means that 25% of the money in the portfolio is invested in the foreign stock mutual fund. It is possible to define the decision variables to represent the actual dollar amount invested in each mutual fund or stock. Redefine the decision variables so that now each variable represents the dollar amount invested in the mutual fund. Assume an investor has $50,000 to invest and wants to minimize the variance of his or her portfolio subject to a constraint that the portfolio returns a minimum of 10%. (a) Reformulate the model given by (8.10) through (8.19) based on the new definition of the decision variables. min ((R1 − R)2 + (R2 − R)2 + (R3 − R)2 + (R4 − R)2 + (R5 − R)2) s.t. R1 =…A factory manufactures both toy boats and toy trucks. It costs $125 to make a toy boat and $175 to make a toy truck. The factory only has $3,000 available to put into their production. If B is the number of boats made, and T is the number of trucks made, which of the following will be a Lagrangian equation if you are trying to maximise profits? a.120 + 5B + 7T = 0 b.120 - 5B - 7T = 0 c.0 = 120 - 5B + 7T d.0 = -120 - 5B - 7T e.120 + 5B - 7T = 0
- A drug company is considering investing $100 million today to bring a weight loss pill to the market. At the end of one year, the firm will know the payoff; there is a 0.50 probability that the pill will sell at a high price and generate $37 million per year of profit forever and a 0.50 probability that the pill will sell at a low price and generate $I million per year of profit forever. The interest rate is 10%. Suppose the firm decides to wait one year to determine whether the pill will sell at a high or low price. The firm will not invest if it learns that the pill will sell at a low price. What is the net present value of waiting one year to make the investment?O $88 millionO$122.72 millionO $201.22 millionO $64.5 millionClancy has difficulty finding parking in his neighborhood and, thus, is considering the gamble of illegally parking on the sidewalk because of the opportunity cost of the time he spends searching for parking. On any given day, Clancy knows he may or may not get a ticket, but he also expects that if he were to do it every day, the average amount he would pay for parking tickets should converge to the expected value. If the expected value is positive, then in the long run, it will be optimal for him to park on the sidewalk and occasionally pay the tickets in exchange for the benefits of not searching for parking. Suppose that Clancy knows that the fine for parking this way is $100, and his opportunity cost (OC) of searching for parking is $20 per day. That is, if he parks on the sidewalk and does not get a ticket, he gets a positive payoff worth $20; if he does get a ticket, he ends up with a payoff ofWhen a famous painting becomes available for sale, it is often known which museum or collector will be the likely winner. Yet, the auctioneer actively woos representatives of other museums that have no chance of winning to attend anyway. Suppose a piece of art has recently become available for sale and will be auctioned off to the highest bidder, with the winner paying an amount equal to the second highest bid. Assume that most collectors know that Valerie places a value of $15,000 on the art piece and that she values this art piece more than any other collector. Suppose that if no one else shows up, Valerie simply bids $15,000/2=$7,500 and wins the piece of art. The expected price paid by Valerie, with no other bidders present, is $________.. Suppose the owner of the artwork manages to recruit another bidder, Antonio, to the auction. Antonio is known to value the art piece at $12,000. The expected price paid by Valerie, given the presence of the second bidder Antonio, is $_______. .
- You are provided five quarters of sales (Q1 = $2,500, Q2 = $2,100, Q3 = $1,900, Q4 = $2,000, and Q5 = $2,300). The moving average for those 5 quarters of sales would be? Multiple Choice $2,160 $2,300 $2,150 $2,000You are taking a multiple-choice test that awards you one point for a correct answer and penalizes you 0.25 points for an incorrect answer. If you have to make a random guess and there are five possible answers, what is the expected value of guessing? Group of answer choices -0.25. 0.25. 0.5. 1. 0.Pick an answer for Q3 and Q9.