a. Explanation Given info: The actual weight of a rock specimen is W and the measured weights are X 1 and X 2 , with X 1 = W + E 1 and X 2 = W + E 2 . The E i ’s are independent of each other and of W , with V ( E 1 ) = V ( E 2 ) = σ E 2 . Calculation: Covariance: The covariance between two random variables, U and V is given as: C o v ( U , V ) = E ( U V ) + E ( U ) E ( V ) , provided the expectations exist. Correlation coefficient: The correlation coefficient between two random variables U and V is given as: ρ = C o r r ( U , V ) = C o v ( U , V ) V ( U ) V ( V ) , provided the expectations exist. Now, V ( X 1 ) = V ( W + E 1 ) = V ( W ) + V ( E 1 ) , as W and E 1 are independent . = σ W 2 + σ E 2 . Similarly, V ( X 2 ) = V ( W + E 2 ) = V ( W ) + V ( E 2 ) , as W and E 2 are independent b. To determine Find ρ when σ W = 1 kg and σ E = 0.01 kg .

WEBASSIGN ACCESS FOR PROBABILITY & STATS

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ISBN: 9780357893111

Author: DEVORE

Publisher: CENGAGE L

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Chapter 5, Problem 93SE

To determine

Express the correlation coefficient ρ between X1 and X2 in terms of the variance of the actual weight σW2 and that of the measured weight σX2.

To determine

Find ρ when σW=1 kg and σE=0.01 kg.

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Chapter 5, Problem 92SE

Chapter 5, Problem 94SE

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Chapter 5 Solutions

WEBASSIGN ACCESS FOR PROBABILITY & STATS

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Express the correlation coefficient ρ between X 1 and X 2 in terms of the variance of the actual weight σ W 2 and that of the measured weight σ X 2 .

Solution Summary: The author explains the correlation coefficient rho between the actual and measured weights of a rock specimen.

Express the correlation coefficient ρ between X1 and X2 in terms of the variance of the actual weight σW2 and that of the measured weight σX2.

Find ρ when σW=1 kg and σE=0.01 kg.

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Chapter 5 Solutions