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A shipping company handles containers in three different sizes: (1) 27 ft³ (3 × 3 × 3), (2) 125 ft³ and (3) 512 ft3. Let Xi (i = 1,2,3) denote the number of type i containers shipped during a given week. With E(X) and σ = var(Xi), suppose that the mean values and standard deviations are as follows: = = H1200, μ2 = 250, μз = 100 3 01 =10, 0212, 03 = 8. 12,03 (a) Assuming that X1, X2, X3 are independent, calculate the expected value and variance of the total volume shipped. [Hint: Volume =27X1+125X2 + 512X3.] (b) Would your calculations necessarily be correct if the X,'s were not independent? Explain.

A shipping company handles containers in three different sizes: (1) 27 ft³ (3 × 3 × 3), (2) 125 ft³ and (3) 512 ft3. Let Xi (i = 1,2,3) denote the number of type i containers shipped during a given week. With E(X) and σ = var(Xi), suppose that the mean values and standard deviations are as follows: = = H1200, μ2 = 250, μз = 100 3 01 =10, 0212, 03 = 8. 12,03 (a) Assuming that X1, X2, X3 are independent, calculate the expected value and variance of the total volume shipped. [Hint: Volume =27X1+125X2 + 512X3.] (b) Would your calculations necessarily be correct if the X,'s were not independent? Explain.

MATLAB: An Introduction with Applications
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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A shipping company handles containers in three different sizes: (1) 27 ft³ (3 × 3 × 3), (2) 125 ft³ and (3) 512 ft3. Let Xi (i = 1,2,3) denote the number of type i containers shipped during a given week. With E(X) and σ = var(Xi), suppose that the mean values and standard deviations are as follows: = = H1200, μ2 = 250, μз = 100 3 01 =10, 0212, 03 = 8. 12,03 (a) Assuming that X1, X2, X3 are independent, calculate the expected value and variance of the total volume shipped. [Hint: Volume =27X1+125X2 + 512X3.] (b) Would your calculations necessarily be correct if the X,'s were not independent? Explain.
Transcribed Image Text:A shipping company handles containers in three different sizes: (1) 27 ft³ (3 × 3 × 3), (2) 125 ft³ and (3) 512 ft3. Let Xi (i = 1,2,3) denote the number of type i containers shipped during a given week. With E(X) and σ = var(Xi), suppose that the mean values and standard deviations are as follows: = = H1200, μ2 = 250, μз = 100 3 01 =10, 0212, 03 = 8. 12,03 (a) Assuming that X1, X2, X3 are independent, calculate the expected value and variance of the total volume shipped. [Hint: Volume =27X1+125X2 + 512X3.] (b) Would your calculations necessarily be correct if the X,'s were not independent? Explain.
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