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 ?i = E(Xi) and ?i2 = V(Xi), suppose that the mean values and standard deviations are as follows:?1 = 210 ?2 = 250 ?3 = 140?1 = 9?2 = 12?3 = 7(a) Assuming that X1, X2, X3 are independent, calculate the expected value and variance of the total volume shipped. [Hint: Volume = 27X1 + 125X2 + 512X3.]

The given volume is Volume=27X1+125X2+512X3. The given mean values and standard deviations are, μ1=210,μ2=250,μ3=140,σ1=9,σ2=12,σ3=7. Also, it is given that μi=EXi and σi2=VXi.(a) The expected value of the total volume shipped is, EVolume=E27X1+125X2+512X3=27EX1+125EX2+512EX3=27×210+125×250+512×140=5,670+31,250+71,680=108,600 Therefore, the expected value of the total volume shipped is 108,600.The variance of the total volume shipped is, VVolume=V27X1+125X2+512X3=272VX1+1252VX2+5122VX3=272×92+1252×122+5122×72=59,049+2,250,000+12,845,056=15,154,105 Therefore, the variance of the total volume shipped is 15,154,105.

Answered: A shipping company handles containers…

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 X_i (i = 1, 2, 3) denote the number of type i containers shipped during a given week. With ?_i = E(X_i) and ?_i² = V(X_i), suppose that the mean values and standard deviations are as follows:

?₁ = 210	?₂ = 250	?₃ = 140
?₁ = 9	?₂ = 12	?₃ = 7

(a) Assuming that X₁, X₂, X₃ are independent, calculate the expected value and variance of the total volume shipped. [Hint: Volume = 27X₁ + 125X₂ + 512X₃.]

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