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A shipping company handles containers in three different sizes: (1) 27 ft3 (3 x 3 x 3), (2) 125 ft³, and (3) 512 ft3. Let X; (i = 1, 2, 3) denote the number of type i containers shipped during a given week. With uj = E(X¡) and o? = v(X¡), suppose that the mean values and standard deviations are as follows: H1 = 200 H2 = 260 H3 = 110 01 = 9 02 = 13 03 = 6 (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 not be correct, but the variance would be correct. O Neither the expected value nor the variance would be correct. O The expected value would be correct, but the variance would not be correct. O Both the expected value and the variance would be correct. Need Help? Read It

A shipping company handles containers in three different sizes: (1) 27 ft3 (3 x 3 x 3), (2) 125 ft³, and (3) 512 ft3. Let X; (i = 1, 2, 3) denote the number of type i containers shipped during a given week. With uj = E(X¡) and o? = v(X¡), suppose that the mean values and standard deviations are as follows: H1 = 200 H2 = 260 H3 = 110 01 = 9 02 = 13 03 = 6 (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 not be correct, but the variance would be correct. O Neither the expected value nor the variance would be correct. O The expected value would be correct, but the variance would not be correct. O Both the expected value and the variance would be correct. Need Help? Read It

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
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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 = 1, 2, 3) denote the number of type i containers shipped during a given week. With uj = E(X¡) and o? = v(X¡), suppose that the mean values and standard deviations are as follows: H1 = 200 H2 = 260 H3 = 110 01 = 9 02 = 13 03 = 6 (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 not be correct, but the variance would be correct. O Neither the expected value nor the variance would be correct. O The expected value would be correct, but the variance would not be correct. O Both the expected value and the variance would be correct. Need Help? Read It
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 X; (i = 1, 2, 3) denote the number of type i containers shipped during a given week. With uj = E(X¡) and o? = v(X¡), suppose that the mean values and standard deviations are as follows: H1 = 200 H2 = 260 H3 = 110 01 = 9 02 = 13 03 = 6 (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 not be correct, but the variance would be correct. O Neither the expected value nor the variance would be correct. O The expected value would be correct, but the variance would not be correct. O Both the expected value and the variance would be correct. Need Help? Read It
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