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You are given two components, component A and component B, and suppose their lifetimes, in hours, are expo- nential with parameters XA and AB, respectively. Further, assume that their lifetimes are independent. (a) If AA AB = 1/25, how many hours, on average, does the component that lives longer outlive the other component by? (b) If AA 1/25 and AB = 1/20, what is the probability component A outlives component B?

You are given two components, component A and component B, and suppose their lifetimes, in hours, are expo- nential with parameters XA and AB, respectively. Further, assume that their lifetimes are independent. (a) If AA AB = 1/25, how many hours, on average, does the component that lives longer outlive the other component by? (b) If AA 1/25 and AB = 1/20, what is the probability component A outlives component B?

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.8: Probabilities Of Disjoint And Overlapping Events
Problem 2C
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You are given two components, component A and component B, and suppose their lifetimes, in hours, are expo- nential with parameters XA and AB, respectively. Further, assume that their lifetimes are independent. (a) If AA AB = 1/25, how many hours, on average, does the component that lives longer outlive the other component by? (b) If AA 1/25 and AB = 1/20, what is the probability component A outlives component B?
Transcribed Image Text:You are given two components, component A and component B, and suppose their lifetimes, in hours, are expo- nential with parameters XA and AB, respectively. Further, assume that their lifetimes are independent. (a) If AA AB = 1/25, how many hours, on average, does the component that lives longer outlive the other component by? (b) If AA 1/25 and AB = 1/20, what is the probability component A outlives component B?
Expert Solution
Step 1

According to the provided data,

А exp В ~ еxp(23)
Step 2

a. The concept of memory less property is used here, that is, if X~exp(λ), then P(X>t+s|X>s) = e-dt. Therefore, even elapsing or expanding ‘s’ unit of time X still follows exponential distribution.

So, on average the component that lives longer compare to other component have still an exponential distribution with rate 1/25. The average is,

E(X) 1 1/25 = 25 hours
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