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If X is an unbiased measurement of a true value Pg, and U(X) is a nonlinear function of X, then in most cases U is a biased estimate of the true value U(Hz). In most cases this bias is ignored. If it is important to reduce this bias, however, a bias-corrected estimate is U(X) – (1/2)(PU /dx . In general the bias-corrected estimate is not unbiased, but has a smaller bias than U(X). Assume that the radius of a circle is measured to be r = 3.0 + 0.1 cm. Estimate the area A, and find the uncertainty in the estimate, without bias correction. Compute the bias-corrected estimate of A. Compare the difference between the bias-corrected and non-bias-corrected estimates to the uncertainty in the non-bias-corrected estimate. Is bias coIrection important in this case? Explain. a. b. C.

If X is an unbiased measurement of a true value Pg, and U(X) is a nonlinear function of X, then in most cases U is a biased estimate of the true value U(Hz). In most cases this bias is ignored. If it is important to reduce this bias, however, a bias-corrected estimate is U(X) – (1/2)(PU /dx . In general the bias-corrected estimate is not unbiased, but has a smaller bias than U(X). Assume that the radius of a circle is measured to be r = 3.0 + 0.1 cm. Estimate the area A, and find the uncertainty in the estimate, without bias correction. Compute the bias-corrected estimate of A. Compare the difference between the bias-corrected and non-bias-corrected estimates to the uncertainty in the non-bias-corrected estimate. Is bias coIrection important in this case? Explain. a. b. C.

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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If X is an unbiased measurement of a true value Pg, and U(X) is a nonlinear function of X, then in most cases U is a biased estimate of the true value U(Hz). In most cases this bias is ignored. If it is important to reduce this bias, however, a bias-corrected estimate is U(X) – (1/2)(PU /dx . In general the bias-corrected estimate is not unbiased, but has a smaller bias than U(X). Assume that the radius of a circle is measured to be r = 3.0 + 0.1 cm. Estimate the area A, and find the uncertainty in the estimate, without bias correction. Compute the bias-corrected estimate of A. Compare the difference between the bias-corrected and non-bias-corrected estimates to the uncertainty in the non-bias-corrected estimate. Is bias coIrection important in this case? Explain. a. b. C.
Transcribed Image Text:If X is an unbiased measurement of a true value Pg, and U(X) is a nonlinear function of X, then in most cases U is a biased estimate of the true value U(Hz). In most cases this bias is ignored. If it is important to reduce this bias, however, a bias-corrected estimate is U(X) – (1/2)(PU /dx . In general the bias-corrected estimate is not unbiased, but has a smaller bias than U(X). Assume that the radius of a circle is measured to be r = 3.0 + 0.1 cm. Estimate the area A, and find the uncertainty in the estimate, without bias correction. Compute the bias-corrected estimate of A. Compare the difference between the bias-corrected and non-bias-corrected estimates to the uncertainty in the non-bias-corrected estimate. Is bias coIrection important in this case? Explain. a. b. C.
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