Homework Help is Here – Start Your Trial Now!
Math
Probability
verify that the theorem of total variance (TTV) holds. ronorad

verify that the theorem of total variance (TTV) holds. ronorad

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
See similar textbooks
icon
Related questions
Question
100%

Please just answer problem 10. However, I am going to attach problem 9 because you need it in order to solve problem 10. 

(9) When X, Y have a bivariate normal density with respective means ux, puy, respective variables o7, 07 and correlation p, we have E(X|Y = y) = µx + pox (y – HY), Var(X|Y = y) = ož(1 – p²). OY Verify the theorem of total expectation (TTE). The following verifications are proposed. (a) Since Var(X|Y = y) = o7(1 - p²) does not depend on y, therefore, the TTE holds. (b) Since E(X|Y = y) depends only on y, the TTE holds. (c) Since E(X|Y) = µx + 2x (Y – µy), we see that E(E(X|Y)) = ux = E(X). Therefore, 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) (10) For the above problem verify that the theorem of total variance (TTV) holds. The following verifications are proposed. (a) Since Var(Var(X|Y)) = o? = Var(X), the TTV holds. (b) Since p²ožVar(Y) of + of(1 – p²) = ož = Var(X). Var(E(X|Y)) + E(Var(X|Y)) the TTV holds. (c) Since Var(E(X|Y)) = Var(X) = ož, the TTV holds. (d) Since Var(E(X|Y)) = 0 and E(Var(X|Y)) = = Var(X), the TTV holds. (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, puy, respective variables o7, 07 and correlation p, we have E(X|Y = y) = µx + pox (y – HY), Var(X|Y = y) = ož(1 – p²). OY Verify the theorem of total expectation (TTE). The following verifications are proposed. (a) Since Var(X|Y = y) = o7(1 - p²) does not depend on y, therefore, the TTE holds. (b) Since E(X|Y = y) depends only on y, the TTE holds. (c) Since E(X|Y) = µx + 2x (Y – µy), we see that E(E(X|Y)) = ux = E(X). Therefore, 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) (10) For the above problem verify that the theorem of total variance (TTV) holds. The following verifications are proposed. (a) Since Var(Var(X|Y)) = o? = Var(X), the TTV holds. (b) Since p²ožVar(Y) of + of(1 – p²) = ož = Var(X). Var(E(X|Y)) + E(Var(X|Y)) the TTV holds. (c) Since Var(E(X|Y)) = Var(X) = ož, the TTV holds. (d) Since Var(E(X|Y)) = 0 and E(Var(X|Y)) = = Var(X), the TTV holds. (e) None of the above The correct verification is (a) (b) (c) (d) (e) N/A (Select One)
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Fundamental Counting Principle
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON
SEE MORE TEXTBOOKS