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Mathematics Forum
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| Author | Message / Information |
| lanery Quote | Reply | | about renewal process posted on: 12/1/2006 6:21:31 PM 1. A patient arrives at a doctor's office. With probability 1/5 he receives service immediately, while with probability 4/5 his service is deferred an hour. After an hour's wait again with probability 1/5 his needs are serviced instantly or another delay of an hour is imposed and so on. (a). What is the waiting time distribution of the first arrival? (b). What is the distribution of the number of patients who receive service over an 8-hr period assuming the same procedure is followed for every arrival and the arrival pattern is that of a Poisson process with parameter 1. 2. The weather in a certain locale A consists of rainy spells alternating with spells when the sun shines. Suppose that the number of days of each rainy spell is Poisson distributed with parameter 2 and a sunny spell is distributed according to a geometric distribution with mean 7 days. Assume that the successive random durations of rainy and sunny spells are statistically independent variables. In the long run, what is the probability on a given day that it will be raining? |
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