If X1, X2, . . . , Xn are independent and unbiased measurements of true values μ1, μ2, . . . , μn , and U(X1, X2, . . . , Xn) is a nonlinear function of 1, X2, . . . , Xn , then in general U(X1, X2, . . . , Xn) is a biased estimate of the true value U(μ1, μ2, . . . , μn). A bias-corrected estimate is U(X1,

When air enters a compressor at pressure P1 and leaves at pressure P2, the intermediate pressure is given by P3 = ˆšP1P2. Assume that P1 = 8.1 ± 0.1 MPa and P2 = 15.4 ± 0.2 MPa.
a. Estimate P3, and find the uncertainty in the estimate, without bias correction.
b. Compute the bias-corrected estimate of P3.
c. Compare the difference between the bias-corrected and non-bias-corrected estimates to the uncertainty in the non-bias-corrected estimate. Is bias correction important in this case? Explain.

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X2, .... X,) – (1/2)EU/aX;)a},,