a) The probability that the next failure occurs in 27000 hours is computed here as:
therefore 0.6604 is the required probability here.
b) The expected time until the third failure here is computed here as:
= 3*Expected time for one failure
= 3*25,000 = 75,000 hours
Therefore 75,000 hours is the expected time here.
c) As the mean time to failure is 25,000 hours, therefore the mean number of failures in 25,000 hours is given as 1.
The probability that the time until third failure is more than 25,000 hours is computed here as:
= Probability that there is 0,1 or 2 in 25,000 hours period
Therefore 0.9197 is the required probability here.
The time between failures of a laser in a machine, X, is exponentially distributed with a...
sorry it is blurry The time between failures of a laser in a machine, X, is exponentially distributed with a mean of 25,000 hours. In other words, X= (failures/hour). 25,000 Exponential Distribution (pdf): f(x) = 1.e-r, for 2 > 0. (a) What is the probability that the next failure occurs in 27,000 hours? (b) What is the expected time until the third failure? (c) What is the probability that the time until the third failure exceeds 25,000 hours?
The average time between failures of a laser machine is exponentially distributed with a mean of 40,000 hours. a) What is the expected time until 4th failure? b) What is the probability that the time to the 5th failure is greater than 80,000 hours?
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Q3. Each time a machine is repaired it remains "up" for an exponentially distributed time with rate A. It then fails and "down", and its failure is either of two types. If it is a type 1 failure, then the time to repair the machine is exponential with rate μ!, if it is a type 2 failure, then the repair time is exponential with rate H2. Each failure is, independently of the time it took the machine to fail, a...
Suppose that the time (in hours) required to repair a machine is an exponentially distributed random variable with parameter λ=0.8, i.e., mean = 1/lambda. What is (a) the probability that a repair takes less than 77 hours?
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