6 Considerunitshaving reliability functionatRA (+)=RB (t)TO(a)erespectivelyunitsConstantTof type A and type Band,Tb) Iflifetimec) What iswhereof 1/ yearshaving0² = ²2.2 yearsqotherwise.Ois a positive value havingandisapositiveunitsof (years) 2a = 40.5 yearswhat tothe expectedof theunits of type A ?the expected lifetime of the writs ofShow thatx =type B?xa6

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Answered: 6 Consider having A R₂ (+) RB (a)…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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lie L- 17 13. A random sample of boots worn by 36 soldiers in a desert region showed an average Jke of 1:08 vears with a standard deviation of 0-6 years. Under the standard conditions, the boots are Inown to have an average life of1·28 years. Is there a reason to assert, at 1% level of significance, that use in desert causes the mean life of such boots to decrease ? What will be your conclusion if the level of significance is 5% ? Assame that the life of boots is normally distributed.
Consider the following time series data for the real consumption of households and government, at current PPPS (in billions 2017USS). In year 2018, the first lagged value of the real consumption is and the first difference is_ Year 2015 2016 2017 2018 2019 1 3 4 5 rcon, | 1267|| 1307 1375 1413 A. 1307; -38 B. 1375; 38. O C.unknown; unknown. D. 1413; unknown
Suppose the mean monthly return on a T-Bill is 0.5% with a standard deviation of 0.58%. Sup-pose we have another investment Y with a 1.5% mean monthly return and standard deviationof 6%. Which of the two investments o ers less risk in terms of investment.
3. Time intervals (in minutes) X₁,..., Xn between successive eruptions of a geyser are modeled as X₂ Exponential (A), where A (> 0) is the eruption rate per minute. We want to report a plausible range for the median interval time. (d) 0 Find the MLE of A. (b) (c) Construct an approximate 95% confidence interval for A using the asymptotic distri- bution of AMLE. (Hint: use the approximation method for confidence interval) i.i.d. N = The median of the Exponential(A) distribution, denoted by 8, is a function of A as (log 2)/λ 0.693/A. Calculate an approximate 95% confidence interval for the median interval time using the Delta method. Find the Fisher information of A. -
Weekly downtime of internet services from an internet service provider (in hours) has expected value 0.5 and variance 0.25. Based on past experience, the data scientist of a retailer store has calculated the loss function to the store from the downtime as C=30X+2X2 where X is the amount of weekly downtime and C is cost. Find the Expected cost, i.e, E(C).
If the expected return on the market is 8% and the risk for your rate is 4%. What is the expected return for a stock with a beta equal to 2.00?
Let X denote the distance (m) that an animal moves from its birth site to the first territorial vacancy it encounters. Suppose that for banner-tailed kangaroo rats, X has an exponential distribution with parameter ? = 0.01422. (b) What is the probability that distance exceeds the mean distance by more than 2 standard deviations? (Round your answer to four decimal places.)(c) What is the value of the median distance? (Round your answer to two decimal places.)
An insurer insures a risk for which individual claim sizes (in £000s) have mean 500 and standard deviation 250. The insurer arranges excess of loss reinsurance for this risk with a retention limit of £1,000,000. Calculate the proportion of claims from this risk for which the insurer expects to receive a payment from the reinsurer if the loss distribution is: (a) gamma (b) lognormal.
Today, the waves are crashing onto the beach every 6 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 6 seconds. Round to 4 decimal places where possible. The probability that the wave will crash onto the beach between 0.6 and 1.7 seconds after the person arrives is P(0.6 < x < 1.7) = The probability that it will take longer than 2.8 seconds for the wave to crash onto the beach after the person arrives is P(x > 2.8) = Suppose that the person has already been standing at the shoreline for 0.7 seconds without a wave crashing in. Find the probability that it will take between 3.2 and 3.8 seconds for the wave to crash onto the shoreline.
2 The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponential distribution with mean 100 cfs (cubic feet per second). (a) Find the probability that the demand will exceed 250 cfs during the early afternoon on a randomly selected day. (Round your answer to four decimal places.) (b) What water-pumping capacity, in cubic feet per second, should the station maintain during early afternoons so that the probability that demand will exceed capacity on a randomly selected day is only 0.02? (Round your answer to two decimal places.) cfs
6
Suppose that the index model for stocks A and B is estimated from excess returns with the following results: RA= 2.0% + 0.40RM + eA RB = -1.8%+ 0.9RM + eB OM = 15%; R-squareA = 0.30; R-squareB = 0.22 What is the standard deviation of each stock? Note: Do not round intermediate calculations. Round your answers to 2 decimal places. Stock A Stock B Standard Deviation % %

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