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(b) Use rules of variance to obtain an expression for the variance and standard deviation (standard error) of the estimator in part (a). V - ) - V) + vn 82.3655 19 -vVX - 82.3655 19

(b) Use rules of variance to obtain an expression for the variance and standard deviation (standard error) of the estimator in part (a). V - ) - V) + vn 82.3655 19 -vVX - 82.3655 19

A First Course in Probability (10th Edition)
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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I am having trouble with section (b) as I had previously got 

2.9668/n1 + o2^2/20 and 82.3655/n1 + 02^2/19. Both are worng

 

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 7.4 8.5 8.9 9.8 9.7 14.1 12.6 11.3 Prior to obtaining data, denote the beam strengths by X,, Xm and the cylinder strengths by 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 n° H, 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) = µ1 – H2 - O EX – ) = (E() – E()) : - = H1 - H2 E(X – Y) = nm( E(X) – E()) = H1 - H2 O E(X – Y) E(X) – E(Y) = H1 - H2 = V - ЕX) - Е(Y) O E(X – Y) = H1 - H2 nm Calculate the estimate for the given data. (Round your answer to three decimal places.) |-0.485 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) + V(M) =ox² + oy 82.3655 19 n1 OX - y = V V(X ) 82.3655 + 19 n1 Compute the estimated standard error. (Round your answer to three decimal places.) 0.572 MPа (c) Calculate a point estimate of the ratio,/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.) 7.302 MPa?
Transcribed Image Text: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 7.4 8.5 8.9 9.8 9.7 14.1 12.6 11.3 Prior to obtaining data, denote the beam strengths by X,, Xm and the cylinder strengths by 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 n° H, 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) = µ1 – H2 - O EX – ) = (E() – E()) : - = H1 - H2 E(X – Y) = nm( E(X) – E()) = H1 - H2 O E(X – Y) E(X) – E(Y) = H1 - H2 = V - ЕX) - Е(Y) O E(X – Y) = H1 - H2 nm Calculate the estimate for the given data. (Round your answer to three decimal places.) |-0.485 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) + V(M) =ox² + oy 82.3655 19 n1 OX - y = V V(X ) 82.3655 + 19 n1 Compute the estimated standard error. (Round your answer to three decimal places.) 0.572 MPа (c) Calculate a point estimate of the ratio,/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.) 7.302 MPa?
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