Question

[6.9] It is estimated that the time for a failure in electronic equipment to occur follows an exponential distribution. Assume that on average 1 failure occurs every 5 years. a) Calculate the probability that the failure will occur after the first year. b) Calculate the probability that the failure will occur after the second year since it did not fail during the first year. c) Calculate the probability that the failure will occur after the third year since it did not fail during the first two years

Answer 1

We are given the average rate of failure here as 1 in 5 years, therefore the average waiting time here is 5 years. Therefore the distribution given here is:

a) The probability here is computed as:

Therefore 0.8187 is the required probability here.

b) The probability here is computed as:

Given that it did not fail in the first year, probability that it will blow after 2 years that is another 1 year is computed here as probability that it occurs after 1 year ( memoryless property of exponential distribution )

Therefore 0.8187 is the required probability here.

c) Again using the same memoryless property of exponential distribution, we will get the exact same probability here.

Therefore 0.8187 is the required probability here.