Please assist with this question fully Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type.5.6 7.2 7.3 6.3 8.1 6.8 7.0 7.6 6.8 6.5 7.0 6.3 7.9 9.08.7 8.7 7.8 9.7 7.4 7.7 9.7 8.0 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 6.6 8.3 7.0 8.68.0 8.1 7.4 8.5 8.9 9.8 9.7 14.1 12.6 12.0Prior to obtaining data, denote the beam strengths by X₁,..., Xm and the cylinder strengths by Y₁ Y. Suppose that the X;'s constitute a random sample from adistribution with mean μ, and standard deviation, 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 - M₂.ⒸE(X) = E(X) - E(X) = μ₁ −μ²₂E(X) - E(X)nmO E(X-) == μ₁ - 1₂O E(X)=√E(X) - E(Y) = μ₁ - H²₂2¸ E(X − ¯) = nm(E(X) — E() = μ-= μ₁-H₂|○ E(X − ¯) = (E(X) - E(ñ)² = µ₁ −μ²₂²₂Calculate the estimate for the given data. (Round your answer to three decimal places.)-1.2803X 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(5)= 0x² +0,²₁ox-y=√V(x-n₁02Compute the estimated standard error. (Round your answer to three decimal places.)441X MPa(c) Calculate a point estimate of the ratio ₁/₂ of the two standard deviations. (Round your answer to three decimal places.)81998X(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 andcylinder strength. (Round your answer to two decimal places.)7.3934X MPa ²

Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type. 5.6 7.2 7.3 6.3 8.1 6.8 7.0 7.6 6.8 6.5 7.0 6.3 7.9 9.0 8.7 8.7 7.8 9.7 7.4 7.7 9.7 8.0 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 8.6 8.0 8.1 7.4 8.5 8.9 9.8 9.7 14.1 12.6 12.0 Prior to obtaining data, denote the beam strengths by X₁, Xm and the cylinder strengths by Y₁..., Y. Suppose that the X/'s constitute a random sample from a distribution with mean μ₁ and standard deviation and that the Y's form a random sample (independent of the X's) from another distribution with mean μ₂ and standard deviation 2. (a) Use rules of expected value to show that X - Y is an unbiased estimator of #₁ -M₂. ⒸE(X) = E(X) – E(X) = μ₁ - H₂ E(X) - E(X) nm O E(X-) = = H₂-H₂ O E(X)= √E(X) - E(Y) = μ₁ - 1₂ ¸ E(X - 5) = nm(E(X) – E(\)) = μ₁ - M₂ |○ E(X − 1) = (E(X) - E(ñ)² = = μ₁ - H₂ Calculate the estimate for the given data. (Round your answer to three decimal places.) -1.2803 XMPa

Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type. 5.6 7.2 7.3 6.3 8.1 6.8 7.0 7.6 6.8 6.5 7.0 6.3 7.9 9.0 8.7 8.7 7.8 9.7 7.4 7.7 9.7 8.0 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 8.6 8.0 8.1 7.4 8.5 8.9 9.8 9.7 14.1 12.6 12.0 Prior to obtaining data, denote the beam strengths by X₁, Xm and the cylinder strengths by Y₁..., Y. Suppose that the X/'s constitute a random sample from a distribution with mean μ₁ and standard deviation and that the Y's form a random sample (independent of the X's) from another distribution with mean μ₂ and standard deviation 2. (a) Use rules of expected value to show that X - Y is an unbiased estimator of #₁ -M₂. ⒸE(X) = E(X) – E(X) = μ₁ - H₂ E(X) - E(X) nm O E(X-) = = H₂-H₂ O E(X)= √E(X) - E(Y) = μ₁ - 1₂ ¸ E(X - 5) = nm(E(X) – E(\)) = μ₁ - M₂ |○ E(X − 1) = (E(X) - E(ñ)² = = μ₁ - H₂ Calculate the estimate for the given data. (Round your answer to three decimal places.) -1.2803 XMPa

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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Question

Please assist with this question fully

Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type.
5.6 7.2 7.3 6.3 8.1 6.8 7.0 7.6 6.8 6.5 7.0 6.3 7.9 9.0
8.7 8.7 7.8 9.7 7.4 7.7 9.7 8.0 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 8.6
8.0 8.1 7.4 8.5 8.9 9.8 9.7 14.1 12.6 12.0
Prior to obtaining data, denote the beam strengths by X₁,..., Xm and the cylinder strengths by Y₁ Y. Suppose that the X;'s constitute a random sample from a
distribution with mean μ, and standard deviation, and that the Y's form a random sample (independent of the X,'s) from another distribution with mean ₂ and standard
deviation ₂.
(a) Use rules of expected value to show that X - Y is an unbiased estimator of μ₁ - M₂.
ⒸE(X) = E(X) - E(X) = μ₁ −μ²₂
E(X) - E(X)
nm
O E(X-) =
= μ₁ - 1₂
O E(X)=√E(X) - E(Y) = μ₁ - H²₂2
¸ E(X − ¯) = nm(E(X) — E() = μ
-
= μ₁-
H₂
|○ E(X − ¯) = (E(X) - E(ñ)² = µ₁ −μ²₂²₂
Calculate the estimate for the given data. (Round your answer to three decimal places.)
-1.2803
X 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(5)
= 0x² +0,²
₁
ox-y=√V(x-n
₁
02
Compute the estimated standard error. (Round your answer to three decimal places.)
441
X MPa
(c) Calculate a point estimate of the ratio ₁/₂ of the two standard deviations. (Round your answer to three decimal places.)
81998
X
(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.)
7.3934
X MPa ²

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