5.5 7.2 7.3 6.3 8.1 6.8 7.0 7.0 6.8 6.5 7.0 6.3 7.9 9.0 8.6 8.7 7.8 9.7 7.4 7.7 9.7 8.0 7.7 11.6 11.3 11.8 10.7 data below give accompanying strength observations for cylinders. 6.3 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 11.6 r 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 di 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,. Use rules of expected value to show that X- Y is an unbiased estimator of u, - p,. O EX - ) = (E) - E(ñ) = H1- H2 O E(X - Y) = V E(X) – E(Y) = H1 - 42 O EX - ) = E(X) - E(Y) = H1- 42 nm
5.5 7.2 7.3 6.3 8.1 6.8 7.0 7.0 6.8 6.5 7.0 6.3 7.9 9.0 8.6 8.7 7.8 9.7 7.4 7.7 9.7 8.0 7.7 11.6 11.3 11.8 10.7 data below give accompanying strength observations for cylinders. 6.3 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 11.6 r 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 di 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,. Use rules of expected value to show that X- Y is an unbiased estimator of u, - p,. O EX - ) = (E) - E(ñ) = H1- H2 O E(X - Y) = V E(X) – E(Y) = H1 - 42 O EX - ) = E(X) - E(Y) = H1- 42 nm
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
Transcribed Image Text:Consider 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
7.0
6.8
6.5
7.0
6.3
7.9
9.0
8.6
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.
6.3
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
11.6
., Xm and the cylinder strengths by Y,, .., Yo. Suppose that the X's constitute a random sample from a distribution with mean u,
Prior to obtaining data, denote the beam strengths by X,,
and standard deviation o,
and that the Y,'s form a random sample (independent of the X's) from another distribution with mean µ, and standard deviation o,.
(a) Use rules of expected value to show that X – Y is an unbiased estimator of µ, - Hg.
EX – ) = (E(X) - EC)
= H1 - 42
O E(X – )
= V E(X) - E(Y) = H1 - H2
E(X) – E(Y)
-
O E(X – ):
= H1 - H2
nm
O E(X – Y) = nm E(X) – E(Y) = H1 - H2
O E(X – Y) = E(X) – E(Y) = µ1 - H2
Calculate the estimate (in MPa) for the given data. (Round your answer to three decimal places.)
MPа
(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(n
+
Identify the next step in this rule from the options below.
02
+
O vX – Y)
n1
n2
O vx - )
01
02
n1
n2
01
02
O vix - )
n1
n2
2
O viX - Y) =
01
+
n1
n2
Since standard deviation is the square root of variance, it follows that
ox - ỹ = V
V(X - Y)
01
O ox - = V
02
n1
n2
02
O ox - =
n1
n2
2
01
02
O ox - =
n1
n2
2
01
02
O ox - =
+
n1
n2
Compute the estimated standard error (in MPa). (Round your answer to three decimal places.)
MPа
(c) Calculate a point estimate of the ratio o, / 0, of the two standard deviations. (Round your answer to three decimal places.)
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