Assignment:
For the pressure transducer mentioned in Problem below, use the failure rate function to estimate the likelihood that a transducer that has been operating for six years fails in the seventh year. How close is the approximation to the exact answer?
A pressure transducer regulates a climate control system in a factory. The transducer fails according to an exponential distribution with rate one failure every five years on average.
a. What is the cumulative distribution function of the time until failure?
b. What is the probability that a transducer chosen at random functions for eight years without failure?
c. What is the probability that a transducer that has functioned for eight years continues to function for another eight years?
Provide complete and step by step solution for the question and show calculations and use formulas.