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a. Suppose the lifetime X of a component, when measured in hours, has a gamma distribution with parameters a and
b. Let Y = the lifetime measured in minutes. Derive the pdf of Y.If X has a gamma distribution with parameters a and b, what is the probability distribution of Y = cX?
certain kinds of tumors tend to recur. the following data represent the lengths of time in months for a tumor to
A large industrial firm allows a discount on any invoice that is paid within 30 days. Of all invoices, 10% receive the discount. In a company audit, 15 invoices are sampled at random. The mean (average) value of the number of the 15 sampled invoic..
In our example of research on lipstick, where E = $2 and S = $29, what sample size would we require if we desired a 99 percent confidence level? What about if we keep the 95 percent confidence level, but decide that our acceptable error is $4?
A personnel manager has a computer-generated list of all employees that indicates that 70 percent are full-time employees, 20 percent are part-time employees, and 10 percent are furloughed or laid-off employees.
a company that manufacturers coffee for use in commercial machines monitors the caffeine content in its coffee. the
Assume you want to repeat the FDA experiment to achieve an estimation of the mean μ of the amount of caffeine content of a cup of coffee.
The marketing manager of a company that manufactures and distributes farming equipment (such as combine harvesters, ploughs and tractors) recorded the number of farming units sold quarterly for the period 2008 to 2011.
If the trash ag manufacturer hopes to obtain a sample mean that is at least 50 pounds which sample size n=5 or n=40 would be best.
a two factory research is used to evaluate the effectiveness of a new blood pressure medicine. in this two factor study
The average cost of repairing a VCR is $80 with a standard deviation of 19. if one VCR is repaired, find the probability the cost is between 70 and 90.
A production process produces 90% non-defective parts. A sample of 10 parts from the production process is selected. What is the probability that the sample will contain 7 non-defective parts?
Let Z1, Z2,... be iid random variables with density f . Suppose that P(Zi > 0) = 1 and that λ = limx↓0 f (x) > 0. Let Xn = n min{Z1,..., Zn}. Show that Xn """ Z where Z has an exponential distribution with mean 1/λ.
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