Answer the following questions below for an insurance benefit with an expected present value equal to: а) 'Write down in integral form the formula for the expected present value. b) You are given a constant force of interest 8, and a mortality model Px with constant force of mortality µ. Derive an expression for Ax:āj in terms of & and H.
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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.To see the effect of a relatively small error in the estimate of the amount of carbon-14 in a sample being dated, consider this hypothetical situation: a. A bone fragment found in central Illinois in the year 2000 contains 17% of its original carbon-14 content. Estimate the year the animal died. b. Repeat part (a), assuming 18% instead of 17%. c. Repeat part (a), assuming 16% instead of 17.A researcher hypothesizes that in a certain country the net annual growth of private sector purchases of government bonds, B, is positively related to the nominal rate of interest on the bonds, NI, and negatively related to the rate of inflation Π: Bt = a0 + a1NIt + a2Π t + ut Note that it may be hypothesized that B depends on the real rate of interest on bonds, R, where R = NI – Π. Using a sample of 56 annual observations, s/he estimates the following equations: (1) Bt = 0.43 + 0.90NIt - 0.97Πt R21 = 0.962, SSR1 = 2.20, QRESET(F1,52) = 16.6 (3.58) (8.80) (-1.05) (2) Bt = 0.44 + 0.94Rt R22 = 0.960, SSR2 = 2.22, QRESET(F1,53) = 0.9 (9.70) (16.7) (3) Bt = 0.44 + 1.14NIt SSR3 = 9.20, QRESET(F1,53) = 59.9 (8.84) (36.1) (4) NIt = 0.08 + 0.94Πt R24 = 0.997, SSR4 = 0.18, QRESET(F1,53) = 1.4…
- Kaitlyn measures the upload speed in megabits per second of her home broadband internet connection during peak hours and off-peak hours. The results are provided in the accompanying table. Peak Off-Peak 5.83 5.14 6.05 6.80 7.14 6.98 3.54 5.77 5.45 7.27 5.90 6.62 5.81 6.19 4.82 6.08 6.37 6.59 4.65 5.58 5.30 7.41 6.48 6.26 5.96 6.37 5.79 6.31 6.84 6.55 5.06 4.95 5.61 7.03 6.45 6.77 Examine the results of Kaitlyn's test to determine the statements that compare the medians and interquartile ranges of the data sets to each other in terms of this situation. Select the two correct answers. The median upload speed during peak hours is 5.905 megabits per second, which is less than the median upload speed during off-peak hours, 7.005 megabits per second. The upload speeds during peak hours are slower on average compared to off-peak times. The median upload speed during peak hours is 6.37 megabits per second, which is greater than the median upload speed during…1.Suppose that the weight of a type of organism is governed by a power law relationship with its length from snout to tail and the thickness of its central vertebraeResearchers interested in lead exposure due to car exhaust sampled the blood of 52 police officers subjected to constant inhalation of automobile exhaust fumes while working traffic enforcement in a primarily urban environment. The blood samples of these officers had an average lead concentration of 124.32 µg/l and a SD of 37.74 µg/l; a previous study of individuals from a nearby suburb, with no history of exposure, found an average blood level concentration of 35 µg/l. Based on your preceding result, without performing a calculation, would a 99% confidence interval for the average blood concentration level of police officers contain 35 µg/l? Based on your preceding result, without performing a calculation, would a 99% confidence interval for this difference contain 0? Explain why or why not.
- Salaries are usually reviewed annually. Suppose that aunion negotiates a pay increase of 5% for its members.If inflation is running at 4%, how much better off are the unionmembers?An editorial in the New York Times on Sunday June 4, 2011 dicussed the redesigned fuel economy stickers to be required on new cars starting in 2013. Consider a new idsize fuord fusion s model. At $4-a-gallon gas, annual fuel costs would be about $2,200 for 15,000 miles driven... And thats for a car with a rated mileage of 34.9m.p.g. actual highway mileage, as with all vehicles, is lower, in this case about 27m.p.g. Industry clearly needs to do better. Did the times use the rated or the actual mileage in its computation?Refer to Exercise 6. Assume that c = 448 J/kg°C and ΔQ = 1210 J are known with negligible uncertainty. Assume the mass is m = 0.75 ± 0.01 kg. Estimate ΔT, and find the relative uncertainty in the estimate.
- You have received a radioactive mass that is claimed to have a mean decay rate of at least 1 particle per second. If the mean decay rate is less than 1 per second, you may return the product for a refund. Let X be the number of decay events counted in 10 seconds. a) If the mean decay rate is exactly 1 per second (so that the claim is true, but just barely), what is P(X ≤ 1)? b) Based on the answer to part (a), if the mean decay rate is 1 particle per second, would one event in 10 seconds be an unusually small number? c) If you counted one decay event in 10 seconds, would this be convincing evidence that the product should be returned? Explain. d) If the mean decay rate is exactly 1 per second, what is P(X ≤ 8)? e) Based on the answer to part (d), if the mean decay rate is 1 particle per second, would eight events in 10 seconds be an unusually small number? f) If you counted eight decay events in 10 seconds, would this be convincing evidence that the product should be returned? Explain.The owner of a newsstand in a college community estimates the weekly demand for a certain magazine as follows. QuantityDemanded 10 11 12 13 14 15 Probability 0.15 0.30 0.05 0.25 0.10 0.15 Find the number of issues of the magazine that the newsstand owner can expect to sell per week. (Enter your answer to two decimal places.) issuesShow that the equivalent nominal interest and discount rates j(m) and d(m) the relationships consistent with the previous results.