x)=1,2,..., 6. lculate the mean and variance of the number o library to a borrower. dom variable S(t) denotes the total number of e interval (0, t], where t is measured in hours. lculate the mean and variance of the number o norning (9 am-12 noon). lculate the index of dispersion for the random (t); t ≥ 0}, and comment on what your value to
x)=1,2,..., 6. lculate the mean and variance of the number o library to a borrower. dom variable S(t) denotes the total number of e interval (0, t], where t is measured in hours. lculate the mean and variance of the number o norning (9 am-12 noon). lculate the index of dispersion for the random (t); t ≥ 0}, and comment on what your value to
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![Borrowers leave the issue desk of a small library according to a Poisson
process with rate 40 per hour. The number of books issued to a
borrower has a uniform distribution with probability mass function
x=1,2,..., 6.
px(x)=
(a) Calculate the mean and variance of the number of books issued by
the library to a borrower.
The random variable S(t) denotes the total number of books issued in
the time interval (0, t], where t is measured in hours.
(b) Calculate the mean and variance of the number of books issued in
a morning (9 am-12 noon).
(c) Calculate the index of dispersion for the random process
{S(t); t >0}, and comment on what your value tells you about the
pattern of book-borrowing at the library.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3fdf0c29-4228-41d5-88b7-4774a7018544%2F35749f41-4b7a-45d2-9be0-1b83a1f1e3cc%2Fcad0a9d_processed.png&w=3840&q=75)
Transcribed Image Text:Borrowers leave the issue desk of a small library according to a Poisson
process with rate 40 per hour. The number of books issued to a
borrower has a uniform distribution with probability mass function
x=1,2,..., 6.
px(x)=
(a) Calculate the mean and variance of the number of books issued by
the library to a borrower.
The random variable S(t) denotes the total number of books issued in
the time interval (0, t], where t is measured in hours.
(b) Calculate the mean and variance of the number of books issued in
a morning (9 am-12 noon).
(c) Calculate the index of dispersion for the random process
{S(t); t >0}, and comment on what your value tells you about the
pattern of book-borrowing at the library.
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