3. A machine has n components, the lifetimes of which are independent. However the wholemachine will fail if any component fails. The hazard functions for the components arenh1(t),..., hn(t). Show that the hazard function for the machine ish:(t).4. Suppose that the lifetime distributions of the components in Exercise 3 are Weibull distributionswith scale parameters p1,..., Pn and a common index (i.e. "shape parameter") y so that thehazard function for component i is yp:(pit)"-1. Find the lifetime distribution for the machine.

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Answered: 3. A machine has n components, the…

A First Course in Probability (10th Edition)

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Author:Sheldon Ross

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Chapter1: Combinatorial Analysis

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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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3. A machine has n components, the lifetimes of which are independent. However the whole machine will fail if any component fails. The hazard functions for the components are h1(t),..., hn(t). Show that the hazard function for the machine is h(t).