Answered: As soon as one components fails, the…

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

ChapterCSR: Contents Of Student Resources

Section: Chapter Questions

Problem 11.19EP

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Question

As soon as one components fails, the entire system will fail. Suppose each component has a lifetime that is exponentially distributed with ? = 0.01 and that components fail independently of one another. Define events A_i = {ith component lasts at least t hours}, i = 1, . . . , 5, so that the A_is are independent events. Let X = the time at which the system fails—that is, the shortest (minimum) lifetime among the five components.

P(X ≥ t)?

F(t) = P(X ≤ t)?

the pdf of X?

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Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.

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