In statistics, the quantities x = 1 n (x1 + x2 ++ xn) and s2 x = 1 n 1 (x1 x )2 + (x2 x

Chapter 7, Problem 33

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In statistics, the quantities x = 1 n (x1 + x2 ++ xn) and s2 x = 1 n 1 (x1 x )2 + (x2 x )2 ++ (xn x)2 are called, respectively, the sample mean and sample variance of x = (x1, x2,...,xn). (a) Express the quadratic form s2 x in the matrix notation xT Ax, where A is symmetric. (b) Is s2 x a positive definite quadratic form? Explain.