A device contains three components, each of which has a lifetime in hours with the pdf SEE IMAGE FOR PROBLEM 6. (Section 5.3) A device contains three components, each of which has a lifetime in hours2xwith the pdf f(x) =102e (10), 0 < x < o. The device fails if any of its componentsfail. Assuming independent lifetimes, what is the probability that the device fails withinits first hour of operation? Hint: G(y) = P(Y < y) = 1 – P(Y > y) = 1 –P(all three > y) where Y is the minimum lifetime of the three components.

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Answered: 5. (Section 5.3) A device contains…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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A device contains three components, each of which has a lifetime in hours with the pdf SEE IMAGE FOR PROBLEM

6. (Section 5.3) A device contains three components, each of which has a lifetime in hours
2x
with the pdf f(x) =
102
e (10), 0 < x < o. The device fails if any of its components
fail. Assuming independent lifetimes, what is the probability that the device fails within
its first hour of operation? Hint: G(y) = P(Y < y) = 1 – P(Y > y) = 1 –
P(all three > y) where Y is the minimum lifetime of the three components.

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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