A pressure transducer regulates a climate control system in a factory. Thetransducer 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?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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
c. What is the probability that a transducer that has functioned for eight years continues to function for another eight years?
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