I need help in figuring out section (b). What have I done wrong? Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type.5.0 7.2 7.3 6.3 8.1 6.8 7.0 7.5 6.86.57.06.37.9 9.08.9 8.7 7.8 9.7 7.4 7.7 9.7 7.8 7.7 11.6 11.3 11.8 10.7The data below give accompanying strength observations for cylinders.6.8 5.8 7.8 7.1 7.2 9.2 6.68.37.08.77.4 8.1 7.4 8.5 8.9 9.8 9.7 14.1 12.6 11.3Prior to obtaining data, denote the beam strengths by X,,..., Xm and the cylinder strengths by Y, ..., Y. Suppose that the X's constitute a random sample from a distribution with mean u, and standard deviation o, and that the Y's form a random sample (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 u, - H.O E(X - Y) = E(X) – E(Y) = H1 - HzO E(X - ) = (E(X) – E(ñ)= H1 - H2E(X - ) = nm( EX) - E()= 41 -H2O E(X - Y) = v E(X) – E(Y) = Hy - H2O E(X – Y)E(X) – E(Y)= 41 - 42nmCalculate the estimate for the given data. (Round your answer to three decimal places.)-0.485MPa(b) Use rules of variance to obtain an expression for the variance and standard deviation (standard error) of the estimator in part (a).v(X - Y) = V(X) + V()= ox + oy22.9668°220n1X -7 =V V(X )2.966820Compute the estimated standard error. (Round your answer to three decimal places.)0.572V MPa(c) Calculate a point estimate of the ratio o,/0, of the two standard deviations. (Round your answer to three decimal places.)0.827(d) Suppose a single beam and a single cylinder are randomly selected. Calculate a point estimate of the variance of the difference X - Y between beam strength and cylinder strength. (Round your answer to two decimal places.)7.302v MPa?

Given, x: beam strengths 5.0, 7.2, 7.3, 6.3, 8.1, 6.8, 7.0, 7.5, 6.8, 6.5, 7.0, 6.3, 7.9, 9.0, 8.9,…

Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type. 5.0 7.2 7.3 6.3 8.1 6.8 7.0 7.5 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 7.8 7.7 11.6 11.3 11.8 10.7 The data below give accompanying strength observations for cylinders. 6.8 5.8 7.8 7.1 7.2 9.2 6.6 8.3 7.0 8.7 7.4 8.1 74 8.5 8.9 9.8 9.7 14.1 12.6 11.3 rior to obtaining data, denote the beam strengths by X....X and the cylinder strengths by Yg.....Y Suppose that the Xs constitute a random sample from a distribution with mean , and standard deviation e, and that th (a) Use rules of expected value to show that X- Yis an unbiased estimator of - o e -n- VEO - En --2 O E -- - etn Calculate the estimate for the given data. (Round your answer to three decimal places.) (b) Use rules of variance to obtain an expression for the variance and standard deviation (standard error) of the estimator in part (a). vũ -n- vn + vn

Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type. 5.0 7.2 7.3 6.3 8.1 6.8 7.0 7.5 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 7.8 7.7 11.6 11.3 11.8 10.7 The data below give accompanying strength observations for cylinders. 6.8 5.8 7.8 7.1 7.2 9.2 6.6 8.3 7.0 8.7 7.4 8.1 74 8.5 8.9 9.8 9.7 14.1 12.6 11.3 rior to obtaining data, denote the beam strengths by X....X and the cylinder strengths by Yg.....Y Suppose that the Xs constitute a random sample from a distribution with mean , and standard deviation e, and that th (a) Use rules of expected value to show that X- Yis an unbiased estimator of - o e -n- VEO - En --2 O E -- - etn Calculate the estimate for the given data. (Round your answer to three decimal places.) (b) Use rules of variance to obtain an expression for the variance and standard deviation (standard error) of the estimator in part (a). vũ -n- vn + vn

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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