The Central Processing Unit (CPU) in a laptop computer that your company manufactures is known to have the following service life characteristics:

\(P(x>s+t \mid x>s)=P(x>t) \forall s\) and \(\mathrm{t}>0\)

where outcomes, \(x\), of the random variable \(X\) measure the operating life of the CPU, measured in 100,000 hour increments, until failure of the CPU. The engineers in your company tell you that \(E(X)=3\).

(a) Define an appropriate probability model for the experiment of observing the operating life of the CPU until the point of failure.

(b) What is the probability that the CPU fails in the first 100,000 hours of use?

(c) Your company provides a warranty on the CPU stating that you will replace the CPU in any laptop in which the CPU fails within the first 5 years of use. What is the probability that you will be fixing one of the computers that has your CPU in it if the laptop were to be operating 24 hours a day?

(d) The CPU is sold to computer manufacturers at a wholesale price of \(\$ 100\) per CPU. The cost to repair a laptop that has a failed CPU is \(\$ 200\). What is your expected net revenue from the sale of one of these CPUs, taking into account the cost of warranty repair, and assuming as in

(c) that the laptop were operating 24 hours a day?