S 4 Suppose that E(8₂) = E() =1 = 0, var(ô₂) = σ₂², var(§₂) = ₂². Consider thefollowing estimator = a₁ + (1 - a). Find all values of a such that the varianceof estimator 0, is minimal,a. when estimators 0, and 0, are independent.b. when cov(₁,₂)= = c = 0.

Estimator An estimator is a rule for calculating an estimate of a given quantity supported by…

Answered: Suppose that E (0₂) = E(0₂) = = 0,…

A First Course in Probability (10th Edition)

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Author:Sheldon Ross

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Chapter1: Combinatorial Analysis

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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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Based on the following values: Mathematical expectation: E(X) = ∑Xn1 = 1204 = 30 E(Y) = ∑Yn2 = 1884 = 47 E(Z) = ∑Zn3 = 1784 = 44.5 Variance: var(X) = 1n1-1∑X2-1n∑X2 = 14-13678-12024 =26 var(Y) = 1n2-1∑Y2-1n∑Y2 = 14-18890-18824 =18 var(Z) = 1n3-1∑Z2-1n3∑Z2 = 14-18322-17824 =133.6667 Root mean square deviation sd(X)= var(X) =26 = 5.0990 sd(Y)= var(Y) =18 = 4.2426 sd(Z)= var(Z) =133.6667 = 11.5614 Correlation coefficients X Y Z 25 44 28 28 43 48 37 49 55 30 52 47 1. Expectation 120 188 178 2. Variance 26 18 133.6667 3. root mean square deviation 5.099 4.2426 11.5614 Check the hypotheses in the image below, in accordance with the tablic values.
Based on the following values: Mathematical expectation: E(X) = ∑Xn1 = 1204 = 30 E(Y) = ∑Yn2 = 1884 = 47 E(Z) = ∑Zn3 = 1784 = 44.5 Variance: var(X) = 1n1-1∑X2-1n∑X2 = 14-13678-12024 =26 var(Y) = 1n2-1∑Y2-1n∑Y2 = 14-18890-18824 =18 var(Z) = 1n3-1∑Z2-1n3∑Z2 = 14-18322-17824 =133.6667 Root mean square deviation sd(X)= var(X) =26 = 5.0990 sd(Y)= var(Y) =18 = 4.2426 sd(Z)= var(Z) =133.6667 = 11.5614 Correlation coefficients X Y Z 25 44 28 28 43 48 37 49 55 30 52 47 1. Expectation 120 188 178 2. Variance 26 18 133.6667 3. root mean square deviation 5.099 4.2426 11.5614 Check the hypothesis in the image below. The table values are also there

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Suppose that E (0₂) = E(0₂) = = 0, var(0₂) = ₁, var(8₂) = ₂. Consider the following estimator ₂ = a₁ + (1 - a). Find all values of a such that the variance of estimator , is minimal, a. when estimators, and are independent. b. when cov(,,,) = c = 0.