Suppose that X is a random variable whose distribution is completely unknown, but it is known that

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Suppose that X is a random variable whose distribution is completely unknown, but it is known that all the moments E(Xk), for k = 1, 2, . . . , are finite. Suppose also that X1, . . . , Xn form a random sample from this distribution. Show that for k = 1, 2, . . . , the kth sample moment (1/n) is an unbiased estimator of E(Xk).
Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...
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Probability And Statistics

ISBN: 9780321500465

4th Edition

Authors: Morris H. DeGroot, Mark J. Schervish

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