a. Explanation Given info: The lifetime of a component follows a Weibull distribution with the parameters β = 2 and δ = 4 , 000 . Calculation: If the random variable X follows a Weibull distribution. Then the probability density function is, f ( x ) = β δ ( x δ ) β − 1 exp ( − ( x δ ) β ) for x > 0 , δ ( sclae parameter ) > 0 and β ( shape parameter ) > 0 with mean δ Γ ( 1 + 1 β ) and variance V ( X ) = δ 2 Γ ( 1 + 2 β ) − δ 2 [ Γ ( 1 + 1 β ) ] 2 b. To determine Find the value of P ( X > 6 , 000 | X > 3 , 000 ) . c. To determine Compared the results for the exponential distribution.

Applied Statistics and Probability for Engineers

6th Edition

ISBN: 9781118539712

Author: Douglas C. Montgomery

Publisher: WILEY

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Chapter 4.10, Problem 163E

To determine

Find the value of P(X>3,000) .

To determine

Find the value of P(X>6,000|X>3,000) .

To determine

Compared the results for the exponential distribution.

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Chapter 4.10, Problem 162E

Chapter 4.10, Problem 164E

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Chapter 4 Solutions

Applied Statistics and Probability for Engineers

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Find the value of P ( X &gt; 3 , 000 ) .

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Find the value of P(X>3,000) .

Find the value of P(X>6,000|X>3,000) .

Compared the results for the exponential distribution.

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Find the value of P ( X > 3 , 000 ) .