The average time between failures of a laser machine is exponentially distributed with a mean of...
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?
Homework Answers
a)
expected time until 4th failure =4*40000=160000 Hours
b)
expected number of failures in 80,000 hours =80000/40000 =2
therefore probability that the time to the 5th failure is greater than 80,000 hours =P(at most 4 failures in 80,000 hours)
=P(X<=4)=P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)=e-2*20/0!+e-2*21/1!+e-2*22/2!+e-2*23/3!+e-2*24/4!=0.947347
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