Explanation Given: The lifetimes X and Y (in years) of two machine components have joint probability density p ( x , y ) = { 6 125 ( 5 − x − y ) if 0 ≤ x ≤ 5 − y , 0 ≤ y ≤ 5 0 otherwise } Calculation: The probability that both components are still functioning can be determined as: P ( X ≥ 2 , Y ≥ 2 ) = ∫ 2 5 ∫ x = 2 5 − y ( 5 − x − y ) d x d y = 6 125 ∫ 2 5 [ ( 5 − y ) x − x 2 2 ] 2 5 − y d y = 6

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ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 16, Problem 54CRE

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The probability that two machine components are still functioning after 2 years.

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Chapter 16, Problem 53CRE

Chapter 16, Problem 55CRE

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Chapter 16 Solutions

CALCULUS W/SAPLING ACCESS >IC<

Ch. 16.1 - Prob. 1PQ Ch. 16.1 - Prob. 2PQ Ch. 16.1 - Prob. 3PQ Ch. 16.1 - Prob. 4PQ Ch. 16.1 - Prob. 5PQ Ch. 16.1 - Prob. 6PQ Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E

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The probability that two machine components are still functioning after 2 years.

Solution Summary: The author explains how to calculate the probability that two machine components are still functioning after 2 years.

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To calculate: The probability that two machine components are still functioning after 2 years.

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Chapter 16 Solutions

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The probability that two machine components are still functioning after 2 years.