On the average a computer experiences breakdowns every 5 mon

On the average, a computer experiences breakdowns every 5 months. The time until the first breakdown and the times between any two consecutive breakdowns are independent Exponential random variables. After the third breakdown, a computer requires a special maintenance.

a) Compute the probablity that a special maintenance is required within the next 9 months.

b) Given that a special maintenance was not required during the first 12 months, what is the probability that it will not be required within the next 4 months.

Solution

(a) Given X~Exponential distribution with mean=5

F(x)=1-exp(-x/5) for x>0

So the probability is

P(X<9) = 1-exp(-9/5) =0.8347011

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(b)P(X<4|X>12) = P(X<4)

=1-exp(-4/5)

=0.550671