3. The life of a pump follows an exponential distribution with an average life of 800...

3. The life of a pump follows an exponential distribution with an average life of 800 hours. [10]

a) What is the probability that he will die after 900 hours. [10]

b) If the pump has worked for 750 hours without failure, what is the probability that it will fail in the next 100 hours.

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Expert Solution

Note that the average for an exponential distribution is reciprocal of its parameter. Therefore the distribution here is given to be:

a) The probability that he will die after 900 hours is computed here as:

therefore 0.3247 is the required probability here.

b) Exponential distribution follows a memoryless property, therefore it does not matter whether it has worked for x numbers of hours, the probability that it will fail in the next 100 hours remain the same at any time point. It is computed as:

therefore 0.1175 is the required probability here.

orchestra answered 2 years ago

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