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1. A continuous failure time has a density function, fT (t) = β2te-βt (a gamma distribution with first parameter 2). The force of interest is a constant δ. Find expressions in terms of β and δ for: (a) AT‾ ; (b) aT‾ ; (c) the net annual rate of premium payment when premiums are payable continuously prior to failure, for an insurance paying 1 at failure and (d) the reserve at time k for the contract in (c).
2. An insurance contract, based on the failure time T, pays 1 unit at the moment of failure provided this occurs within 5 years. Nothing is paid for failure after that time. The force of interest is a constant 0.1. If T has the hazard functionμT (t) =2/10 - t,
Find the probability that the present value of the benefits is strictly positive, but less than or equal to e-0.3.
An Auditor of a small bsuiness has sampled 50 of 700 accounts. The sample mean total receivables is $435, and the sample standard deviation is $86. Find a 95% confidence interval for the total amount of receivables.
Explain why an observed value of 250 hours is not unusual for an individual light bulb, even though it is outside the confidence interval you calculated.
The mean and standard deviation of these scores are 23.0 and 5.0 respectively. The test was administered to 100 students. What is the T-score equivalent to the raw-score 13?
Show that theta~ = u(X) is an unbiased estimator of theta, where u(0) = 1 and u(x) = 0 if x =1,2, ... Compare the MSEs of theta(hat) and theta~ for estimating theta = e^(-m) when m=1 and m=2
what is the difference between a population linear model and an estimated linear regression
Explain can you find out statistical support in this poll for that statement. When it comes to the war in Iraq, among which of the subsiquent statements comes closer to your point of view.
on friday wall street traders were anxiously awaiting the federal governments release of numbers on the january
Identify a business research topic and Define the research questions for the identified problem or opportunity
Fit a linear trend to this data. Estimate and interpret the coefficients of this model. Does the linear model fit well? Interpret the coefficient of determination and standard error of estimate. Provide three measures of forecast accuracy.
One state lottery has 300 prizes of $1, 65 prizes of $10, 18 prizes of $75, 6 prizes of $325, 2 prizes of $1000, and 1 prize of $2000. Assume that 32,000 lottery tickets are issued and sold for $1.
People in a large population average 60 inches tall. You will take a random sample and will be given a dollar for each person in your sample who is over 65 inches tall. Does the law of average relate to the answer you give?
Here are the questions: Solve the differential equations by separation of variables.
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