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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
Related questions
Question
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6b0becd3-da7d-494c-b3c6-698d5c68dcd8%2Fd5139d8d-a787-4e32-9111-4162ce4c583b%2Fkm5vfce_processed.png&w=3840&q=75)
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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