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A machine is composed of 4 components that work independently and each component has its useful...

A machine is composed of 4 components that work independently and each component has its useful life related to an exponential model with an average of 3 years. It is known that the machine only works when the 4 components are in perfect condition. Determine the machine's service life density. Also calculate the probability that the machine's service life will exceed 4 years

Math   Statistics-And-Probability   
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Answer #1

Let the machine's lifetime random variable be X. For each component we are given the lifetime model here as:

as parameter is the reciprocal of mean here.

The cumulative distributive function for X here is obtained as:

= 1 - Probability that all the components work for at least time x.

The PDF for X now that is the required density function here is obtained as:

This is the required density function here.

The probability that the machine service life will exceed 4 years is computed here as:

Therefore 0.0048 is the required probability here.

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