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Value at Risk (VAR) has become a key concept in financial calculations. The VAR of an investment is defined as that value v such that there is only a 1 percent chance that the loss from the investment will be greater than v.
(a) If the gain from an investment is a normal random variable with mean 10 and variance 49 determine the VAR. (If Xis the gain, then -Xis the loss.)
(b) Among a set of investments all of whose gains are normally distributed, show that the one having the smallest VAR is the one having the largest value of µ - 2.33s, where µ and s are the mean and variance of the gain from the investment.
Composite sampling is a way to reduce laboratory testing costs. A public healthdepartment is testing for possible fecal contamination in public swimming pools. In thiscase, water samples from 5 pools are combined for one test.
What is the value of μ for the network? What is the value of σμ2 for the network? What is the probability that this network can be finished within 27 days?
Did the support representative explain the process for resolving your problem? Did the support representative keep you informed about the status of progress in resolving your problem?
If the manufacturer's claim is true, what is the probability that the claim will be rejected?
The manager of The Cheesecake Factory in Boston reports that on six randomly selected weekdays, the number of customers served was 120, 130, 100, 205, 185, and 220. She believes that the number of customers served on weekdays follows a normal dist..
Using the terminology of this chapter, what name applies to each of the boldface numbers in the following quotes (e.g., odds, risk, relative risk)?
The Empirical Rule and Chebychev's Inequality both relate the percent of data points to the number of standard deviations above or below the mean.
Compute SSE, SST, and SSR. Compute the coefficient of determination r^2. Comment on the goodness of fit. Compute hte sample correlation coefficient
A major application of analytics in marketing is determining the attrition of customers. Suppose that the probability of a long-distance carrier's customer leaving for another carrier from one month to the next is 0.12.
Estimate the true mean price for this particular model with 95% confidence?
What does a confidence interval tell us and why is it importance to use a confidence interval?
Briefly explain how increasing sample size influences each of the following. Assume that all other factors are held constant.
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