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Question: The Pareto distribution with parameter a > 0 has PDF f(x) = a/xa+1 for x 1 (and 0 otherwise). This distribution is often used in statistical modeling.
(a) Find the CDF of a Pareto r.v. with parameter a; check that it is a valid CDF.
(b) Suppose that for a simulation you want to run, you need to generate i.i.d. Pareto(a) r.v.s. You have a computer that knows how to generate i.i.d. Unif(0, 1) r.v.s but does not know how to generate Pareto r.v.s. Show how to do this.
A bottling company fills bottles with a mean of 500 mL of liquid, with a standard deviation of 2 mL. Quality control randomly samples 20 bottles at a time. Consider the mean volume of liquid in the sample bottles. What is the mean of the sampling ..
Test this problem at 99% confidence and provide conclusion. Would the problem have a similar conclusion if we knew the population standard deviation was $40,000? Why?
Data were collected from 60 students who took both college entrance exams. The mean SAT score was with a standard deviation of. The mean ACT score was with a standard deviation of. The linear correlation coefficient between the two scores equals r..
a researcher wishes to test the hypothesis that the mean age at first marriage for women in texas is less than 24. in a
Industry standards recommend that 9 percent of new vehicles need warranty service in the first year. Determine the probability that none of these vehicles needs warranty service?
suppose that a device stops working if one of its five components fails and suppose that the lifetimes of the five
Calculate the probability that the sample proportion for the follow-up study will be between 0.48 and 0.60._______ Calculate the probability that the sample proportion for the study will be less than 0.40._______
Explain why the statement is incorrect. RETAIL SALES Mark Owens, an optician, estimates that the probability that a customer coming into his store.
The amount of money spent by a customer is uniformly distributed over (0,100). Find the mean and variance of the amount of money that the store takes on a given day.
A company has 80 of these cars in its fleet. Let represent the mean CO level for the company's fleet.
However, argue why this isn't really fair to you, that is, argue why your expected winnings are negative.
Let X be the random variable which counts the number of cars that, in a given unit of time, pass by Joe's Barber Shop on Main Street. What is the distribution of X?
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