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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.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter2: Exponential, Logarithmic, And Trigonometric Functions
Section2.CR: Chapter 2 Review
Problem 111CR: Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data...
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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 µ; = E(X;) and o? = v(X;), suppose that the mean values and standard deviations are as follows: H1 = 230 Hz = 240 H3 = 120 01 = 9 02 = 12 03 = 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.
Transcribed Image Text: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 µ; = E(X;) and o? = v(X;), suppose that the mean values and standard deviations are as follows: H1 = 230 Hz = 240 H3 = 120 01 = 9 02 = 12 03 = 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.
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