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(9) When X, Y have a bivariate normal density with respective means ux, HY , respective variables o, of and correlation p, we have E(X|Y = y) = µx + oy po X (y - HY), Var(X|Y = y) = o3 (1 – p'). Verify the theorem of total expectation (TTE). The following verifications are proposed. (a) Since Var(X|Y = y) = o}(1 – p²) does not depend on y, therefore, the TTE holds. (b) Since E(XY (c) Since E(X|Y) = 4x + X (Y – µy), we see that E(E(XY))= 4x = E(X). Therefore, the TTE holds. y) depends only on y, the TTE holds. oy (d) TTE does not hold. (e) None of the above The correct verification is (a) (b) (c) (d) (e) N/A (Select One)

(9) When X, Y have a bivariate normal density with respective means ux, HY , respective variables o, of and correlation p, we have E(X|Y = y) = µx + oy po X (y - HY), Var(X|Y = y) = o3 (1 – p'). Verify the theorem of total expectation (TTE). The following verifications are proposed. (a) Since Var(X|Y = y) = o}(1 – p²) does not depend on y, therefore, the TTE holds. (b) Since E(XY (c) Since E(X|Y) = 4x + X (Y – µy), we see that E(E(XY))= 4x = E(X). Therefore, the TTE holds. y) depends only on y, the TTE holds. oy (d) TTE does not hold. (e) None of the above The correct verification is (a) (b) (c) (d) (e) N/A (Select One)

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter4: Writing Linear Equations
Section: Chapter Questions
Problem 12CR
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(9) When X, Y have a bivariate normal density with respective means ux: HY, respective variables o, o and correlation p, we have po x (y – HY), oy Var(X|Y = y) = ož(1 – p*). E(X|Y = y) = µx + Verify the theorem of total expectation (TTE). The following verifications are proposed. (a) Since Var(X|Y = y) = o} (1 p) does not depend on y, therefore, the TTE holds. (b) Since E(XY = y) depends only on y, the TTE holds. (c) Since E(X|Y) = µx + X (Y Hy), we see that E(E(X|Y)) = ux = E(X). Therefore, the TTE holds. (d) TTE does not hold. (e) None of the above The correct verification is (a) (b) (c) (d) (e) N/A (Select One)
Transcribed Image Text:(9) When X, Y have a bivariate normal density with respective means ux: HY, respective variables o, o and correlation p, we have po x (y – HY), oy Var(X|Y = y) = ož(1 – p*). E(X|Y = y) = µx + Verify the theorem of total expectation (TTE). The following verifications are proposed. (a) Since Var(X|Y = y) = o} (1 p) does not depend on y, therefore, the TTE holds. (b) Since E(XY = y) depends only on y, the TTE holds. (c) Since E(X|Y) = µx + X (Y Hy), we see that E(E(X|Y)) = ux = E(X). Therefore, the TTE holds. (d) TTE does not hold. (e) None of the above The correct verification is (a) (b) (c) (d) (e) N/A (Select One)
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