Question

The life of automobile voltage regulators follows an exponential distribution with an average
of 6 years. You buy a car with 6 years of use, with a voltage regulator that is functional,
and plan to stay with the vehicle for an additional 6 years.
a) What is the probability that the voltage regulator will fail during the time that you kept
the car?
b) If the regulator fails 3 years after you bought the vehicle and it is replaced, what is
the average time until it fails again?

Answer 1

a)

Let X = life time of the regulator

X follow exponential with rate 1/6

P(X < 6) = 1 -e^(-1/6 *6) = 1-1/e = 0.6321

b)

E(X) = 1/$\lambda$ = 1/(1/6) = 6 years

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