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. (Round your answers to four decimal places.) (a) If ?1 = ?2 = ?3 = 60 and ?12 = ?22 = ?32 = 18, calculate P(To ≤ 204) and P(144 ≤ To ≤ 204). P(To ≤ 204) = P(144 ≤ To ≤ 204) = (b) Using the ?i's and ?i's given in part (a), calculate both P(54 ≤ X) and P(58 ≤ X ≤ 62). P(54 ≤ X) = P(58 ≤ X ≤ 62) = (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) =
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. (Round your answers to four decimal places.) (a) If ?1 = ?2 = ?3 = 60 and ?12 = ?22 = ?32 = 18, calculate P(To ≤ 204) and P(144 ≤ To ≤ 204). P(To ≤ 204) = P(144 ≤ To ≤ 204) = (b) Using the ?i's and ?i's given in part (a), calculate both P(54 ≤ X) and P(58 ≤ X ≤ 62). P(54 ≤ X) = P(58 ≤ X ≤ 62) = (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) =
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Question
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. (Round your answers to four decimal places.)(a)
If
?1 = ?2 = ?3 = 60
and
?12 = ?22 = ?32 = 18,
calculate
P(To ≤ 204)
and
P(144 ≤ To ≤ 204).
P(To ≤ 204)
=
P(144 ≤ To ≤ 204)
= (b)
Using the
?i's
and
?i's
given in part (a), calculate both
P(54 ≤ X)
and
P(58 ≤ X ≤ 62).
P(54 ≤ X)
=
P(58 ≤ X ≤ 62)
=(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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