Q1. In this question we will prove Proposition 4.1.3 from the notes. Suppose that X = (X₁,..., Xp) is a random vector taking values in RP, and that E[[X²] <∞. (a) Prove that we may write Cov(X) = E[(X-EX)(X - EX)¹]. (b) Citing any results you use from the notes, prove that Tr(vv) = |v|² for any v ERP. (c) Using (a) and (b), show that Р E|X - EX² = Var(X;) = Tr(Cov(X)). i=1
Q1. In this question we will prove Proposition 4.1.3 from the notes. Suppose that X = (X₁,..., Xp) is a random vector taking values in RP, and that E[[X²] <∞. (a) Prove that we may write Cov(X) = E[(X-EX)(X - EX)¹]. (b) Citing any results you use from the notes, prove that Tr(vv) = |v|² for any v ERP. (c) Using (a) and (b), show that Р E|X - EX² = Var(X;) = Tr(Cov(X)). i=1
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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