Question

Suppose X is a random vector, where X = (X(1), . . . , x(d))T , d with mean 0 and covariance matrix vv1 , for some vector v ER 1point possible (graded) Let v = . (i.e., v is the normalized version of v). What is the variance of v X? (If applicable, enter trans(v) for the transpose v of v, and normv) for the norm |vll of a vector v.) Var (V STANDARD NOTATION SubmitYou have used 0 of 3 attempts Save 1 point possible (graded) What is the asymptotic distribution of Xn-2 (Select all that apply.) m-o) N(O.L) where L is the identity matrix in R 2 points possible (graded) Let Y, = ν (VTX, ) , or equivalently v (v . X, ) = (v . X, ) ỹ . We will compare the asymptotic distribution of Xn you obtain in part (d) to the asymptotic distribution of Yn where Y What is the expectation EY of Y,? Choose all that apply. 0 (the zero vector in Rd 0 (the real number zero Find the covariance matrix Σ). of Y, in terms of the vector v. If applicable, enter transtv) for the transpose v" of v, and norm(v) for the norm v of a vector v.)

Answer 1

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