The lifetime of a microprocessor is exponentially distributed with mean 3000 hours.
a. What proportion of microprocessors will fail within 300 hours?
b. What proportion of microprocessors will function for more than 6000 hours?
c. A new microprocessor is installed alongside one that has been functioning for 1000 hours. Assume the two microprocessors function independently. What is the probability that the new one fails before the old one?
Let T be the lifetime of a microprocessor.
(c) Let S represent the time to failure of the new microprocessor, and let T represent the additional time, past the
first 1000 hours, to failure of the old microprocessor. By the lack of memory property, both S and T have the
same exponential distribution. Since S and T are independent, P (S < T) = 1 / 2.
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