Question: 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,

Suppose that X is a random variable whose 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 Show that for k = 1, 2, . . . , the kth sample moment (1/n) is an unbiased estimator of E(Xk).

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