← An investment firm offers its customers municipal bonds that mature after varying numbers of years. Given that the cumulative distribution function of T, the number of years to maturity for a randomly selected bond, is given by F(t), find (a) P(T= 11); (b) P(T> 5); (c) P(2.4

A decision maker has a utility function for monetarygains x given by u(x) (x 10,000)1/2. a Show that the person is indifferent between the sta-tus quo and L: With probability 13, he or she gains $80,000 L: With probability 23, he or she loses $10,000b If there is a 10% chance that a painting valued at$10,000 will be stolen during the next year, what is themost (per year) that the decision maker would be willingto pay for insurance covering the loss of the painting?

(A) Less than 0.6 (B) At least 0.6, but less than 0.7 (C) At least 0.7, but less than 0.8 (D) At least 0.8, but less than 0.9 (E) At least 0.9 An insurer has data on losses for four policyholders for 7 years. The loss from the 1h policyholder for year j is X. You are given: 4 7 É({xy – X,) = 33.60 Σ(Χ- x- 3.30 Using nonparametric empirical Bayes estimation, calculate the Bühlmann credibility factor for an individual policyholder.

In our discussion of Winter’s method, a monthlyseasonality of (say) 0.80 for January means that duringJanuary, air conditioner sales are expected to be 80% of thesales during an average month. An alternative approach tomodeling seasonality is to let the seasonality factor for eachmonth represent how far above average air conditioner saleswill be during the current month. For instance, if sJan 50, then air conditioner sales during January are expectedto be 50 less than air conditioner sales during an averagemonth. If sJuly 90, then air conditioner sales during Julyare expected to be 90 more than air conditioner sales duringan average month. Letst the seasonality for month t after month tdemand is observedLt the estimate of base after month tdemand is observedTt the estimate of trend after month t demandis observedThen the Winter’s method equations given in the text aremodified to be as follows (* indicates multiplication):Lt a * (I ) (1 a) * (Lt1 Tt1)Tt b * (Lt Lt1) (1 b) * Tt1st g *…

Let A Find grad(div( A ) %3D

O Expand the brackets (distribute) (x+i)(x-4)= %3D

Suppose that a decision maker's risk atitude toward monetary gains or losses x given by the utility function(x) = (50,000+x) 34/2. Suppose that a decision maker has the choice of buying a lottery ticket for $5, or not. Suppose that the lottery winning is $1,000,000, and the chance of winning is one in a thousand. Then..... O The decision maker should not buy the ticket, as the utility from not buying is 223.6, and the expected utility from buying is 223.59. The decision maker should not buy the ticket, as the utility from not buying is 223.6067, and the expected utility from buyingis 223.6065. O The decision maker should buy the ticket, as the utility from not buying 223.60, and the utility from buying is 224.4. The decision maker should buy the ticket, as the utility from not buying 223.6065, and the utility from buying is 223.6067.

The maximum patent life for a new drug is 17 years. Subtracting the length of time required by the FDA for testing and approval of the drug provides the actual patent life of the drug-that is, the length of time that a company has to recover research and development costs and make a profit. Suppose the distribution of the lengths of patent life for new drugs is as shown here. Years, x 3 4 5 6 7 8 9 10 0.03 0.07 0.07 0.12 0.18 0.15 0.19 0.10 0.05 0.03 0.01 11 12 13 p(x) (a) Find the expected number of years of patent life for a new drug. 9.55 (b) Find the standard deviation of x. (Round your answer to four decimal places.) (c) Find the probability that x falls into the interval p + 20. Need Help? Read It

Statistics Question

Two investments, X and Y, have the characteristics shown below. E(X) = $60, E(Y) = $90, o = 10,000, o? = 17,000 and axy = 6,500 If the weight of portfolio assets assigned to investment X is 0.8, calculate the a. portfolio expected return and b. portfolio risk. a. If the weight of portfolio assets assigned to investment X is 0.8, the portfolio expected return is $ (Type an integer or a decimal.) b. If the weight of portfolio assets assigned to investment X is 0.8, the portfolio risk is approximately $. (Round to two decimal places as needed.)