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 μ; = E(X;) and σ;² = V(X;), suppose that th mean values and standard deviations are as follows: M₁ = 200 %₁ = 11 = 260 H₂ %₂ = 13 H3 = 110 03 = 7 (a) Assuming that X₁, X₂, X3 are independent, calculate the expected value and variance of the total volume shipped. [Hin 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 Both the expected value and the variance would be correct. 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. The onog o would not be correct
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 μ; = E(X;) and σ;² = V(X;), suppose that th mean values and standard deviations are as follows: M₁ = 200 %₁ = 11 = 260 H₂ %₂ = 13 H3 = 110 03 = 7 (a) Assuming that X₁, X₂, X3 are independent, calculate the expected value and variance of the total volume shipped. [Hin 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 Both the expected value and the variance would be correct. 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. The onog o would not be correct
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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please solve a and b.
![A shipping company handles containers in three different sizes: (1) 27 ft³ (3 × 3 × 3), (2) 125 ft³, and (3) 512 ft³. Let X,
2
(i = 1, 2, 3) denote the number of type i containers shipped during a given week. With µ; = E(X;) and σ,² = V(X;), suppose that the
mean values and standard deviations are as follows:
M1
01
= 200
= 11
= 260
Из
M2
02 = 13 03 =
= 110
= 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.]
ft³
ft6
expected value
variance
(b) Would your calculations necessarily be correct if the X;'s were not independent? Explain.
O Both the expected value and the variance would be correct.
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7afdb6c4-3a61-4c47-91da-dfd2e9ec1a67%2Fd62a79bb-d8df-4860-a241-30993b9957cf%2Fnp8rcrl_processed.png&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,
2
(i = 1, 2, 3) denote the number of type i containers shipped during a given week. With µ; = E(X;) and σ,² = V(X;), suppose that the
mean values and standard deviations are as follows:
M1
01
= 200
= 11
= 260
Из
M2
02 = 13 03 =
= 110
= 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.]
ft³
ft6
expected value
variance
(b) Would your calculations necessarily be correct if the X;'s were not independent? Explain.
O Both the expected value and the variance would be correct.
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.
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