probablity

Charlie joins a new reading club, from which he receives books to read. Suppose that books arrive as a Poisson process at a rate λ of books per week. For each book, the time it takes for Charlie to read it is exponentially distributed with parameter μ; i.e., on average it takes Charlie 1/μ weeks to finish one book. Assume that the reading times for different books are independent, and also independent from the book arrival process.
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.
For all of the parts below, give your answers in terms of μ and λ, using standard notation. Enter μ as "mu" and λ as "lambda".
Hint: When Charlie starts reading a book, the total time he spends on reading it can be viewed as the first arrival from a Poisson process of rate μ, and you can then think about merging or splitting of Poisson processes.
When Charlie starts a new book, what is the probability that he can finish this book without being interrupted by a new book?
??
Given that Charlie receives a new book while reading a book, what is the probability that he can finish both books, the new one and the interrupted one, without further interruption?
??
What is the expected reading time of a book given that it is not interrupted?

  1. 👍 1
  2. 👎 0
  3. 👁 747
  1. Any ideas?

    1. 👍 0
    2. 👎 0
  2. Please help :(

    1. 👍 0
    2. 👎 0
  3. Anyone got this....?

    1. 👍 0
    2. 👎 0
  4. " I found the answers to be
    1.) mu/(mu+lambda)
    2.) (mu/(mu+lambda))^2
    3.) 1/(mu+lambda).
    Sourced from course solutions found on CourseHero for Fall 2016 "

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. 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

    asked by Anonymous on May 8, 2018
  2. Math

    Charlie joins a new reading club, from which he receives books to read. Suppose that books arrive as a Poisson process at a rate λ of books per week. For each book, the time it takes for Charlie to read it is exponentially

    asked by YuLin on December 18, 2018
  3. math

    A class was keeping track of how many books on the summer reading list each student read. Sarah said she read 1⁄3 of the 15 books. Dana said she read 40% of the 15 books. Which statement is true about the number of books the

    asked by shakiya on December 18, 2018
  4. Reading

    Rosalind Wiseman books Terra Elan McVoy books Susane Colasanti books Elizabeth Scott books Wendelin Van Draanen books Laura Preble books Piper Banks books Melissa Kantor books Kate Brian books Katie Finn books Pamela Wells books

    asked by Laruen on November 12, 2011
  5. math

    An English teacher needs to pick 10 books to put on her reading list for the next school year, and she needs to plan the order in which they should be read. She has narrowed down her choices to 5 novels, 5 plays, 4 poetry books,

    asked by anon on February 7, 2019
  1. English

    This club makes videos related to environment. Which club name is suitable for this club? 1. the environment image production club 2. the environmental movie club This club is related to reading books, watching movies, and

    asked by rfvv on May 25, 2018
  2. math statistics

    An English teacher needs to pick 10 books to put on her reading list for the next school year, and she needs to plan the order in which they should be read. She has narrowed down her choices to 5 novels, 5 plays, 4 poetry books,

    asked by mary on February 7, 2019
  3. math

    An English teacher needs to pick 13 books to put on her reading list for the next school year, and she needs to plan the order in which they should be read. She has narrowed down her choices to 5 novels, 7 plays, 7 poetry books,

    asked by jaylon on February 28, 2019
  4. Math

    5. How many more books do you need to read over the summer if you already read 4 books and you need to read a total of 16 books? Write a equation to represent this situation and solve the equation using mental math. A. 16 ÷ b=

    asked by HomeworkStan on October 2, 2019
  5. statistics

    An English teacher needs to pick 10 books to put on her reading list for the next school year and she needs to plan the order in which they should be read. She has narrowed down her choices to 4 novels 8 plays, 5 poetry books, and

    asked by greg on February 10, 2019

More Similar Questions