Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type.7.0 7.2 6.8 6.5 7.0 6.3 7.9 9.09.7 8.1 7.7 11.6 11.3 11.8 10.7observations for cylinders.5.9 7.2 7.3 6.3 8.1 6.88.4 8.7 7.8 9.7 7.4 7.7The data below give accompanying strength6.7 5.8 7.8 7.1 7.2 9.2 6.6 8.3 7.0 8.17.0 8.1 7.4 8.5 8.9 9.8 9.7 14.1 12.6 11.4Prior to obtaining data, denote the beam strengths by X₁,..., Xm and the cylinder strengths by Y₁,..., Y. Suppose that the Xi's constitute a random sample from a distribution with mean ₁ and standard deviation 0₁ and that the Y's form a random sample (independent of the X;'s) from another distribution with mean ₂ and standarddeviation ₂.(a) Use rules of expected value to show that X - Y is an unbiased estimator of μ₁ - μ₂.O E(X)=√E(X) - E(Y) = μ₁ - H₂ⒸE(XY) = E(X) - E(X) = 14₁ 14₂O E(X-= E(X) - E(X) = 11 - 12nmE(X - Y = nm(E(X) - E()) = μ₁ −44₂| E(X) = (E(X) - E(M)² =Calculate the estimate for the given data. (Round your answer to three decimal places.)MPa(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) = V(X) + (5)= 0x² + 0x²01= khi khôox-Y = √V(x - y)n10₂²Compute the estimated standard error. (Round your answer to three decimal places.)MPa(c) Calculate a point estimate of the ratio 0₁/02 of the two standard deviations. (Round your answer to three decimal places.)(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.)MPa²

Given information: X Y 5.9 6.7 7.2 5.8 7.3 7.8 6.3 7.1 8.1 7.2 6.8 9.2 7 6.6 7.2…

Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type. 5.9 7.2 7.3 6.3 8.1 6.8 7.0 7.2 6.8 6.5 7.0 6.3 7.9 9.0 8.4 8.7 7.8 9.7 7.4 7.7 9.7 8.1 7.7 11.6 11.3 11.8 10.7 The data below give accompanying strength observations for cylinders. 6.7 5.8 7.8 7.1 7.2 9.2 6.6 8.3 7.0 8.1 7.0 8.1 7.4 8.5 8.9 9.8 9.7 14.1 12.6 11.4 Prior to obtaining data, denote the beam strengths by X₁X and the cylinder strengths by Y. Y Suppose that the X's constitute a random sample from a distribution with mean and standard deviation and that the Y's form a random sample (independent of the X's) from another distribution with mean and standard deviation d (a) Use rules of expected value to show that X-F is an unbiased estimator of ₂-2- E(X)=√E(X)=E(V)-#₁ - #2 • ECR-5)- 800) - 80-1₂-₂ 0-5-0-0. 0 € - ³) = ² = 4₂-₂ EUX-(C)- () -- O ○ £₁² - ³) - (EU) - ²(ñ)² = P₁-P2 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). vox-5-v+v -07+07 8-9-√VX-5 "1 Compute the estimated standard error. (Round your answer to three decimal places.) (c) Calculate a point estimate of the ratio d/d of the two standard deviations. (Round your answer to three decimal places.) (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.) MP₂²

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...