Charlie joins a new reading club, from which he receives books to read. Suppose that books arrive as a Poisson process with rate λ=1/2 books per week. For each book, suppose that the time it takes for Charlie to finish reading is exponentially distributed with parameter μ=1/3 i.e., on average it takes Charlie 1/μ=3 weeks to finish one book. Assume that the reading times of different books are independent.
The problem with Charlie is that he is easily distracted. If he is reading a book when a new book arrives, he immediately turns to read the new one, and only comes back to the older book when he finishes the new book.
Hint: when Charlie starts reading a book, the finishing time can be viewed as the first arrival from a Poisson process of rate μ=1/3, and you can apply merging and splitting of this Poisson process with other processes.
When Charlie starts a new book, what is the probability that he will finish this book without being interrupted?
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Given that Charlie receives a new book while reading another book, what is the probability that he can finish both books, the new one and the interrupted one, without further interruption?
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What is the average reading time of a book given that it is not interrupted? Hint: The answer is not 1/μ=3.
unanswered
1 answer
1) 0.4
2) 0.16
3) 1.2