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The length of a component is to be estimated through repeated measurement. Ten independent measurements are made with an instrument whose uncertainty is 0.05 a. mm. Let denote the average of these measurements. Find the uncertainty in 7. b. A new measuring device, whose uncertainty is only 0.02 mm, becomes available. Five independent measurements are made with this device. Let y denote the average of these measurements. Find the uncertainty in y. In order to decrease the uncertainty still further, it is decided to combine the estimates X and y. One engineer suggests estimating the length with (1/2)X + (1/2)Y. A second engineer argues that since X is base don 10 measurements, while y is based on only five, a better estimate is (10/15)X+ (5/15)F. Find the uncertainty in each of these C. estimates. Which is smaller? Find the value c such that the weighted average c + (1- c)Y has minimum uncertainty. Find the uncertainty in this weighted average. d.

The length of a component is to be estimated through repeated measurement. Ten independent measurements are made with an instrument whose uncertainty is 0.05 a. mm. Let denote the average of these measurements. Find the uncertainty in 7. b. A new measuring device, whose uncertainty is only 0.02 mm, becomes available. Five independent measurements are made with this device. Let y denote the average of these measurements. Find the uncertainty in y. In order to decrease the uncertainty still further, it is decided to combine the estimates X and y. One engineer suggests estimating the length with (1/2)X + (1/2)Y. A second engineer argues that since X is base don 10 measurements, while y is based on only five, a better estimate is (10/15)X+ (5/15)F. Find the uncertainty in each of these C. estimates. Which is smaller? Find the value c such that the weighted average c + (1- c)Y has minimum uncertainty. Find the uncertainty in this weighted average. d.

MATLAB: An Introduction with Applications
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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The length of a component is to be estimated through repeated measurement. Ten independent measurements are made with an instrument whose uncertainty is 0.05 a. mm. Let denote the average of these measurements. Find the uncertainty in 7. b. A new measuring device, whose uncertainty is only 0.02 mm, becomes available. Five independent measurements are made with this device. Let y denote the average of these measurements. Find the uncertainty in y. In order to decrease the uncertainty still further, it is decided to combine the estimates X and y. One engineer suggests estimating the length with (1/2)X + (1/2)Y. A second engineer argues that since X is base don 10 measurements, while y is based on only five, a better estimate is (10/15)X+ (5/15)F. Find the uncertainty in each of these C. estimates. Which is smaller? Find the value c such that the weighted average c + (1- c)Y has minimum uncertainty. Find the uncertainty in this weighted average. d.
Transcribed Image Text:The length of a component is to be estimated through repeated measurement. Ten independent measurements are made with an instrument whose uncertainty is 0.05 a. mm. Let denote the average of these measurements. Find the uncertainty in 7. b. A new measuring device, whose uncertainty is only 0.02 mm, becomes available. Five independent measurements are made with this device. Let y denote the average of these measurements. Find the uncertainty in y. In order to decrease the uncertainty still further, it is decided to combine the estimates X and y. One engineer suggests estimating the length with (1/2)X + (1/2)Y. A second engineer argues that since X is base don 10 measurements, while y is based on only five, a better estimate is (10/15)X+ (5/15)F. Find the uncertainty in each of these C. estimates. Which is smaller? Find the value c such that the weighted average c + (1- c)Y has minimum uncertainty. Find the uncertainty in this weighted average. d.
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