onsider the accompanying data on flexural strength (MPa) for concrete beams of a certain type. 5.5 7.2 7.3 6.3 8.1 6.8 7.0 7.1 6.8 6.5 7.0 6.3 7.9 9.0 8.9 8.7 7.8 9.7 7.4 7.7 9.7 7.9 7.7 11.6 11.3 11.8 10.7 he data below give accompanying strength observations for cylinders. 6.5 5.8 7.8 7.1 7.2 9.2 6.6 8.3 7.0 8.4 7.1 8.1 7.4 8.5 8.9 9.8 9.7 14.1 12.6 11.5 rior to obtaining data, denote the beam strengths by X,. ....,X, and the cylinder strengths by Y,...., Y. Suppose that the X's constitute a random sample from a distribution with mean u, and standard ample (independent of the X;s) from another distribution with mean u, and standard deviation o. (a) Use rules of expected value to show that X – Y is an unbiased estimator of #, - H2. O EX - - EX) – E(Ý) nm O EX – 7) = (EX) – E()* = "1 = #2 O EX – ) = nm( EX) - E(Y) = ", - H2 • EX – ) = EX) – E(Ÿ) = #1 = H2 O EX – ) = VE(X) – E(Y) = H1 – H2 Calculate the estimate for the given data. (Round your answer to three decimal places.) -0.443 MPa (b) Use rules of variance to obtain an expression for the variance and standard deviation (standard error) of the estimator in part (a). vũ - ) = VX) + V)
onsider the accompanying data on flexural strength (MPa) for concrete beams of a certain type. 5.5 7.2 7.3 6.3 8.1 6.8 7.0 7.1 6.8 6.5 7.0 6.3 7.9 9.0 8.9 8.7 7.8 9.7 7.4 7.7 9.7 7.9 7.7 11.6 11.3 11.8 10.7 he data below give accompanying strength observations for cylinders. 6.5 5.8 7.8 7.1 7.2 9.2 6.6 8.3 7.0 8.4 7.1 8.1 7.4 8.5 8.9 9.8 9.7 14.1 12.6 11.5 rior to obtaining data, denote the beam strengths by X,. ....,X, and the cylinder strengths by Y,...., Y. Suppose that the X's constitute a random sample from a distribution with mean u, and standard ample (independent of the X;s) from another distribution with mean u, and standard deviation o. (a) Use rules of expected value to show that X – Y is an unbiased estimator of #, - H2. O EX - - EX) – E(Ý) nm O EX – 7) = (EX) – E()* = "1 = #2 O EX – ) = nm( EX) - E(Y) = ", - H2 • EX – ) = EX) – E(Ÿ) = #1 = H2 O EX – ) = VE(X) – E(Y) = H1 – H2 Calculate the estimate for the given data. (Round your answer to three decimal places.) -0.443 MPa (b) Use rules of variance to obtain an expression for the variance and standard deviation (standard error) of the estimator in part (a). vũ - ) = VX) + V)
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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