Question: Consider the i.i.d. random variables X1,X2, . . . ,Xn. Show that bk = 1 n Pn i=1 Xk i is an unbiased estimator of

Consider the i.i.d. random variables X1,X2, . . . ,Xn. Show that bk = 1 n Pn i=1 Xk i is an unbiased estimator of the kth moment k = E(Xk); i.e. that E(bk) = k, for any natural number k. Remark: Despite this the parameter estimators that are obtained through the method of moments are sometimes biased (that happens because the functions h1, . . . , hn, where k = h(k), are often nonlinear)

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