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For two independent measurements x = bland x = b2 , the best x should be some weighted

Introduction to Linear Algebra | 4th Edition | ISBN: 9780980232714 | Authors: Gilbert Strang ISBN: 9780980232714 166

Solution for problem 7 Chapter 8.6

Introduction to Linear Algebra | 4th Edition

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Introduction to Linear Algebra | 4th Edition | ISBN: 9780980232714 | Authors: Gilbert Strang

Introduction to Linear Algebra | 4th Edition

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Problem 7

For two independent measurements x = bland x = b2 , the best x should be some weighted average x = ab i + (1 - a)b2 . When bi and b2 have mean zero and variances al and af, the variance of x will be P = a2al + (1 - a )2af. Choose the number a that minimizes P: dP / da = O. Show that this a gives the x in equation (2) which the text claimed is best, using weights WI = l/al and W2 = l/a2'

Step-by-Step Solution:
Step 1 of 3

InEqualities: 9/2/16 -Less than: Less than or equal to Greater than Greater than or equal to AB A≥B Transitivity: -If A0 - D-B>0 - Therefore (D+C) – (A+B) >0 - Therefore D+C > A+B Mult. Of Inequalities: - If A>B…...

Step 2 of 3

Chapter 8.6, Problem 7 is Solved
Step 3 of 3

Textbook: Introduction to Linear Algebra
Edition: 4
Author: Gilbert Strang
ISBN: 9780980232714

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For two independent measurements x = bland x = b2 , the best x should be some weighted

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