Let X and u be (scalar) random variables. Select all of the following statements which are true.O If E(u | X) = 0, then E(u) = 0.O If Cov(X, u) = 0, then X and u are independent.O If E(u | X) = 0, then Cov(X, u) = 0.O If X and u are independent, and E(u) = 0, then E(u | X) = 0.Let B and B' be unbiased estimators of a k x 1 vector of parameters B. Select all of the following statements which implythat B is weakly more efficient than B'.O The variance of a B' is at least as great as the variance of a B for all k x 1 vectors a.O All diagonal entries of the variance matrix of B' - B are nonnegative.O The variance matrix of B' B is positive semidefinite.O The variance of a'ß' is at least as great as the variance of a'ß for some k x 1 vector a.

Solution: am answered only 1st one please re upload 2nd question: 1. First statement: The law of…

Let X and u be (scalar) random variables. Select all of the following statements which are true. O If E(u | X) = 0, then E(u) = 0. O If Cov(X, u) = 0, then X and u are independent. O If E(u | X) = 0, then Cov(X, u) = 0.

Let X and u be (scalar) random variables. Select all of the following statements which are true. O If E(u | X) = 0, then E(u) = 0. O If Cov(X, u) = 0, then X and u are independent. O If E(u | X) = 0, then Cov(X, u) = 0.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.2: Norms And Distance Functions

Problem 52EQ

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Question

Let X and u be (scalar) random variables. Select all of the following statements which are true.
O If E(u | X) = 0, then E(u) = 0.
O If Cov(X, u) = 0, then X and u are independent.
O If E(u | X) = 0, then Cov(X, u) = 0.
O If X and u are independent, and E(u) = 0, then E(u | X) = 0.
Let B and B' be unbiased estimators of a k x 1 vector of parameters B. Select all of the following statements which imply
that B is weakly more efficient than B'.
O The variance of a B' is at least as great as the variance of a B for all k x 1 vectors a.
O All diagonal entries of the variance matrix of B' - B are nonnegative.
O The variance matrix of B' B is positive semidefinite.
O The variance of a'ß' is at least as great as the variance of a'ß for some k x 1 vector a.

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