Let X1, X2, and X3 represent the times necessary to perform three successive repair tasks at a certain service facility. Suppose they are independent, normal rv's with expected values ?1, ?2, and ?3 and variances ?12, ?22, and ?32, respectively. (a) If ?1 = ?2 = ?3 = 70 and ?12 = ?22 = ?32 = 18, calculate P(To ≤ 228) and P(174 ≤ To ≤ 228). P(To ≤ 228)= P(174 ≤ To ≤ 228)= (b) Using the ?i's and ?i's given in part (a), calculate both P(64 ≤ X) and P(68 ≤ X ≤ 72). P(64 ≤ X)= P(68 ≤ X ≤ 72)= (c) Using the ?i's and ?i's given in part (a), calculate P(−12 ≤ X1 − 0.5X2 − 0.5X3 ≤ 6). P(−12 ≤ X1 − 0.5X2 − 0.5X3 ≤ 6) =

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Answered: Let X1, X2, and X3 represent the times necessary to perform three successive repair tasks at a certain service facility. Suppose they are independent, normal…

MATLAB: An Introduction with Applications

6th Edition

ISBN: 9781119256830

Author: Amos Gilat

Publisher: John Wiley & Sons Inc

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Question

Let X₁, X₂, and X₃represent the times necessary to perform three successive repair tasks at a certain service facility. Suppose they are independent, normal rv's with expected values ?₁, ?₂, and ?₃and variances ?₁², ?₂², and ?₃², respectively.

(a) If ?₁ = ?₂ = ?₃ = 70 and ?₁² = ?₂² = ?₃² = 18, calculate

P(T_o ≤ 228)

and

P(174 ≤ T_o ≤ 228).

P(T_o ≤ 228)=

P(174 ≤ T_o ≤ 228)=

(b) Using the

?_i's and ?_i's given in part (a), calculate both P(64 ≤ X) and P(68 ≤ X ≤ 72).

P(64 ≤ X)=

P(68 ≤ X ≤ 72)=

?_i's and ?_i's given in part (a), calculate P(−12 ≤ X₁ − 0.5X₂ − 0.5X₃ ≤ 6).

P(−12 ≤ X₁ − 0.5X₂ − 0.5X₃ ≤ 6) =

(d) Interpret the quantity P(−12 ≤ X₁ − 0.5X₂ − 0.5X₃ ≤ 6).

The quantity represents the probability that the difference between X₁ and the sum of X₂ and X₃ is between −12 and 6.
The quantity represents the probability that the difference between X₁ and the average of X₂ and X₃ is between −12 and 6.
The quantity represents the probability that the difference between X₃ and the sum of X₁ and X₂ is between −12 and 6.
The quantity represents the probability that the difference between X₃ and the average of X₁ and X₂ is between −12 and 6.The quantity represents the probability that X₁, X₂, and X₃ are all between −12 and 6.