The length of time between breakdowns of an essential piece of equipment is impo

Question

The length of time between breakdowns of an essential piece of equipment
is important in the decision of the use of auxiliary equipment. An engineer
thinks that the best "model" for time between breakdowns of a generator
is the exponential distribution with a mean of 15 days.

(a) If the generator has just broken down, what is the probability that it
will break down in the next 21 days?

(b) The generator has already lasted for 15 days, what is the probability
that the generator will operate for another 5 days without a breakdown?

Explanation / Answer

a. 0.7534 equation for cumulative exponential distribution: 1-e^-lambda*x lambda=1/15 x=21 b. conditional probability layered on top of an exponential one probability of lasting 21 days given that we lasted 15 equations are given here http://www.mathgoodies.com/lessons/vol6/conditional.html probability of lasting 15: 0.3679 probability of lasting 15 and 21=probability of 21: 0.2466 probability of lasting 21 given 15: 0.67029084

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