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

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
icon
Related questions
Question

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.
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.
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning