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
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 = 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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F11ad9986-04b0-4336-8340-a3038312afe8%2F92952a2f-266f-4961-aa59-7d795f1e8fcd%2F3ue8bsg_processed.jpeg&w=3840&q=75)
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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