Question

Problem 8-28 The exponential distribution applies to lifetimes of a certain component. Its failure rate is unknown. Find the probability that the component will survive past 5 years assuming:

Answer 1

Answer:

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Problem 8-28 The exponential distribution applies to lifetimes of a certain component. Its failure rate is unknown. Find the probability that the component will survive past 5 years assuming:

(a) lambda=.5

Pr=

(b) lambda=0.9

Pr=

(c) lambda=1.1

Pr=

answer : a) P( X> 5 ) = 0.0821

              b) P( X > 5 ) = 0.0111

              c) P ( X > 5 ) = 0.00409

Step-by-step explanation:

A) P( X > 5 ) = exp ( - λ * x )

   = $e^{-2.5}$ ≈ 0.082

B)  P( X > 5 ) = exp ( - λ * x )  

  = $e^{-4.5}$ ≈ 0.0111

C) P( X > 5 ) = exp ( - λ * x )  

 = $e^{5.5}$  ≈ 0.00409