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**Unformatted text preview: **.5 7.2
8.9 9.2
9.8 6.6
9.7 8.3
14.1 7.0
12.6 8.3
11.2 cylinder strength (Y, 2)
6.1
7.8 5.8
8.1 7.8
7.4 is an unbiased estimator of μ1 – μ2. a) Use the rules of expected value to show that
Calculate the estimate for the given data. We want to show that E(
) = μ 1 – μ2
θ = E(
) = E( ) - E( ) (from 5.8) = μ1 – μ2 (because E( ) = E(X) and E( ) = E(Y) and E(X) and E(Y)
are unbiased)
Therefore, = so = 8.141 – 8.585 = -0.434 = b) Use rules of variance from Chapter 5 to obtain an expression for the variance and standard
deviation (standard error) of the estimator in part (a), and then compute the estimated standard
error.
Since X and Y are independent, and are independent so 3 c) Calculate a point estimate of the ratio σ1/σ2 of the two standard deviations. 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.
Since X and Y are independent, 4...

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