# Probability

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?

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?

What is the average reading time of a book given that it is not interrupted? Hint: The answer is not 1/μ=3.

1. 👍
2. 👎
3. 👁
1. When Charlie starts a new book, what is the probability that he will finish this book without being interrupted?
1) 0.4
2) 0.16
3) 1.2

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2. 👎

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