3. X and Z are two independently distributed standard normal random variables. Y = X2+52. Please calculate E(Y). (A)-1.5 (B) 1 (C) 0.5 (D) 2.5

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.

3. X and Z are two independently distributed standard normal random variables. Y = X²+52. Please calculate E(Y).
(A)-1.5
(B) 1
(C) 0.5
(D) 2.5

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