Cars arrive at a parking location Ccord aing to a Poisson process with rates A. Each arriving passenger is a short-term parker with probability p, or a long-term parker with probability 1-p. The parting times of customers are independent of each other. The parking time of a short-term parker has a uniform distribution on [a1,b1] and that of a long-term parker has a uniform distribution on [a2,b2]. The parking lot has ample capacity.
Cars arrive at a parking location Ccord aing to a Poisson process with rates A. Each arriving passenger is a short-term parker with probability p, or a long-term parker with probability 1-p. The parting times of customers are independent of each other. The parking time of a short-term parker has a uniform distribution on [a1,b1] and that of a long-term parker has a uniform distribution on [a2,b2]. The parking lot has ample capacity.
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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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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![Cars arrive at a parking location according to
a Poisson process with rates A. Each arriving
passenger is a short-term parker with
probability p, or a long-term parker with
probability 1-p. The parting times of
customers are independent of each other.
The parking time of a short-term parker has a
uniform distribution on [a1,b1] and that of a
long-term parker has a uniform distribution
on [a2,b2]. The parking lot has ample capacity.
a. Describe the distribution of a number of
short-term parkers per unit time?
b. What is the mean parking time of an
arriving car?
c. Find the variance of parking time using
conditional variance formula.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4df1412f-98f8-45f1-b949-6e67ef4913aa%2Fd5922858-37d6-4c89-a0b3-003a680e062b%2Fphe38bx_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Cars arrive at a parking location according to
a Poisson process with rates A. Each arriving
passenger is a short-term parker with
probability p, or a long-term parker with
probability 1-p. The parting times of
customers are independent of each other.
The parking time of a short-term parker has a
uniform distribution on [a1,b1] and that of a
long-term parker has a uniform distribution
on [a2,b2]. The parking lot has ample capacity.
a. Describe the distribution of a number of
short-term parkers per unit time?
b. What is the mean parking time of an
arriving car?
c. Find the variance of parking time using
conditional variance formula.
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