A shipping company handles containers in three different sizes: (1) 27 ft (3 x 3 x 3), (2) 125 ft, and (3) 512 ft. Let X; (i = 1, 2, 3) denote the number of type i containers shipped during a given week. With µ; = E(X;) and o? = v(X;), suppose that the mean values and standard deviations are as follows: Hz = 240 02 = 12 H1 = 230 l3 = 120 01 = 9 O3 = 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.] expected value | ft3 variance | ft6 (b) Would your calculations necessarily be correct if the X's were not independent? Explain. O The expected value would be correct, but the variance would not be correct. O Neither the expected value nor the variance would be correct. O The expected value would not be correct, but the variance would be correct. O Both the expected value and the variance would be correct.

A shipping company handles containers in three different sizes: (1) 27 ft (3 x 3 x 3), (2) 125 ft, and (3) 512 ft. Let X; (i = 1, 2, 3) denote the number of type i containers shipped during a given week. With µ; = E(X;) and o? = v(X;), suppose that the mean values and standard deviations are as follows: Hz = 240 02 = 12 H1 = 230 l3 = 120 01 = 9 O3 = 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.] expected value | ft3 variance | ft6 (b) Would your calculations necessarily be correct if the X's were not independent? Explain. O The expected value would be correct, but the variance would not be correct. O Neither the expected value nor the variance would be correct. O The expected value would not be correct, but the variance would be correct. O Both the expected value and the variance would be correct.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

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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