Y is distributed N(0,4), and X is distributed N(0,16). Please calculate B(Y2) and E(X3).(A) E(Y2) = 4 and E(X3) = 16(B) E(Y2) = 2 and E(X3) = 64(C) E(Y2) = 4 and E(X3) =0(D) E(Y2) = 2 and E(X3) = 8(E) None of the above choices (a)-(d).

複選題Consider the vector space S consisting of all degree-2 polynomials with real coefficients, ie., polynomials in the form of c0 +c1t +c2t2. Define the inner product between two vectors as c2d2. Which of the following statement is/are true? (A). The dimension of S is 2. (B). The polynomials 1 + t, t and 1 + t2 are linearly independent. (C). The set{1 + t, t, 1 + t2} can be a basis for S. (D). The two polynomials 1 - 2t + t2, and -1 + 2t - t2 are orthogonal to cach other. (E). None of the above is true.

Y is distributed N(0,4), and X is distributed N(0,16). Please calculate B(Y²) and E(X³).
(A) E(Y²) = 4 and E(X3) = 16
(B) E(Y²) = 2 and E(X3) = 64
(C) E(Y²) = 4 and E(X3) =0
(D) E(Y²) = 2 and E(X3) = 8

(E) None of the above choices (a)-(d).

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