Let a denote the annual premium for a whole life contingent contract of benefit amount 10,000 issued to (30), and let L(7) denote the present value of loss random variable for this con- tract. The interest rate is i.06. Find the smallest value of a such that Pr[L(r) > 0] < .50, given the following values from the life table survival model to which (30) is subject:

Let a denote the annual premium for a whole life contingent contract of benefit amount 10,000 issued to (30), and let L(7) denote the present value of loss random variable for this con- tract. The interest rate is i.06. Find the smallest value of a such that Pr[L(r) > 0] < .50, given the following values from the life table survival model to which (30) is subject:

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter1: Functions

Section1.2: The Least Square Line

Problem 5E

See similar textbooks

Similar questions

Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?
Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.
Consider the following data: Stock M N Average return 26% 16% Risk (Std. Dev.) 20% 10% If the return on stocks M and N are perfectly negatively correlated, what is the range of risk (std dev) associated with all possible portfolio combinations? A. Range of the risk: between 0= risk s10 % OB. Range of the risk: between 0 < risk 10% OC. Range of the risk: between 5% and 10%. OD. Range of the risk (std. dev): between 15% to 20% OE. None of the above
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.
A manufacturing firm, Caleb Corp, produces and sells product in its home (US) market, and in a foreign market. There is inherent risk in the revenues collected from the foreign market due to volatility in the exchange rate. Under a benchmark strategy, all of the production takes place in the home country. The resulting expected profits for Caleb Corp are variable, due to variation in the exchange rate. As an approximation, the firm has estimated profits for five possible ranges of the exchange rate, with profit represented as a lottery, L= (.2, 150; .2, 200; .3, 220; .2,250; .1, 270) The probabilities are estimated probabilities for the different ranges. The outcomes in this lottery are the estimated final profit levels (not changes in profit). (a) Calculate the expected profit if the firm follows this benchmark strategy, i.e., E(L)
The Arrow-Pratt measures of absolute and relative risk aversion respectively describe the willingness of a consumers to risk a fixed amount of wealth or a fixed fraction of their wealth. This problem will demonstrate this by setting up a simple investment problem. Suppose that consumers begin with initial wealth Wo and may buy shares of a risky asset whose payoff per share is given by 2. (1 w/ prob. P, X = 1-1 w/ prob.1– p. Therefore buying { shares of the risky asset yields final wealth W = Wo +X. Suppose that each consumer may buy an unlimited number of shares, and seeks to maximize expected utility of final wealth max E[u(W)]. (a) Expand the consumer's expected utility maximization problem, and find the first order condition. (b) Let Cara be a consumer whose utility function exhibits constant absolute risk aver- sion UA(W) = 1– e-aW Find Cara's optimal number of shares and show that it does not depend on her starting wealth Wo-
A manufacturing firm, Caleb Corp, produces and sells product in its home (US) market, and in a foreign market. There is inherent risk in the revenues collected from the foreign market due to volatility in the exchange rate. Under a benchmark strategy, all of the production takes place in the home country. The resulting expected profits for Caleb Corp are variable, due to variation in the exchange rate. As an approximation, the firm has estimated profits for five possible ranges of the exchange rate, with profit represented as a lottery, L= (.2, 150; .2, 200; .3, 220; .2,250; .1, 270) The probabilities are estimated probabilities for the different ranges. The outcomes in this lottery are the estimated final profit levels (not changes in profit). Now suppose the firm can also buy forward contracts on foreign currency to neutralize the effect of the exchange rate on profits. Assume that these provide complete hedging, but that it involves an additional cost, so that following the…
Suppose that the index model for stocks A and B is estimated from excess returns with the following results: RA = 3% +0.7RM + еA RB = -2% + 1.2RM + eB OM = 20% ; R-squareд = 0.20; R-squareg = 0.12 What is the covariance between each stock and the market index? (Calculate using numbers in decimal form, not percentages. Do not round your intermediate calculations. Round your answers to 3 decimal places.) Stock A Stock B Covariance
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.)
Suppose the likelihood that a child will attend a live theatrical performance can be madeled by a- 0.01(-0.008x + 1.4x + 4) (15 sxs 100). Here, g is the fraction of children with annual household income x thousand dollars wha will attend a live drametic performance at a theater during the year. Compute the income elesticity of demand E at an income level of $20,000. (Round yaur answer to two decimal places.) HINT (See Example 2.1 E- Interpret the result. At a family income level of s 20000 the fraction of children ettending a live theatrical performance is increasing by % per 1% increase in household incame.
1. We obtain the following supply curve of computers from a regression of quantity supplied on price in a market: Q = 7.527 + 0.00063 P, where Q is quantity supplied of computers measured in units, P is price measured in dollars per unit. We know 674.725 and 2930.549. Based on this information, if price increases by one dollar, quantity supplied increases by ____ units. (Only type in the number in your answer, do not type in "units" again.) 2. We obtain the following demand curve of beef in a market: Q = 44506.941 - 3338.553 ln(P), where Q is quantity demanded of beef measured in pounds, P is price measured in dollars per pound. We know 8.781 and 13016.956. Based on this information, if price increases by 1 dollar, quantity demanded decreases by ____%. (Only type in the number in your answer, do not type in the percentage sign "%" again.)