Proposition 312 let x be a random variable and let c

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Unformatted text preview: day before or was finished being repaired 68 CHAPTER 2. DISCRETE-TYPE RANDOM VARIABLES the day before or that it is the first day, the machine is up on the given day with probability 0.999 and it goes down with probability 0.001. If a machine goes down on a given day, then the machine stays down for repair for a total of five days. The two machines go up and down independently. We would like to estimate the mean time until there is a day such that both machines are down. This is a challenging problem. Can you show that the mean time until outage is between 200 and 400 years? Here is a reasonably accurate solution. Given both machines were working the day before, or were just repaired, or it is the first day, the probability that at least one of them fails on a given day is about 0.002. That is, the waiting time until at least one machine goes down is approximately geometrically distributed with parameter p = 0.002. The mean of such a distribution is 1/p, so the mean time until at least one of the machine...
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