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Let x=(x1,,xm)Rm be the outcome of m repeated trials, and we denote the mean by . An empirical estimate of the second-order raw moment is

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Let x=(x1,,xm)Rm be the outcome of m repeated trials, and we denote the mean by . An empirical estimate of the second-order raw moment is m1i=1m(xi2) and a (biased) empirical estimate of the second-order central moment is m1i=1m[(xi)2] Express them in vector representations. In other words, you may use x,, and vector/scalar operators. Summations are not allowed. Here, nth order raw moment is E[Xn] and nth order central moment is E[(X)n]. The definitions per se are not needed for solving the

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