Let xi, i = 1,2,...,n be independent realizations from a population distributed like a Pareto with...

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Let xi, i = 1,2,...,n be independent realizations from apopulation distributed like a Pareto with unknown mean.
(a) Compute the Standard Error of the sample mean. [Note:Byâ€œcomputeâ€, I mean â€œfind the formula forâ€]. What is theprobability that the sample mean is two standard deviations largerthan the popula-
tion mean?
(b) Suppose the sample mean is 1 and the Standard Error is 2.Con- sider a test of the hypothesis that the population mean is 0,against the alternative that it is greater. What is the pâˆ’value?Compute a 5% confidence interval [Note: Use the Normal as anapprox- imation for simplicity]. What is the type II error if theactual population mean is 2?

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a Let and be population mean and population standard deviationrespectivelyLet sample meanStandard error of sample mean isRequired ProbabilityBy using Chebychevs inequality If X is a random variable See Answer

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