7. A clinic opens at 7 AM. Patients arrive at a Poisson rate of five an hour from 7AM until 10AM. They arrive at a Poisson rate of eight an hour between 10AM and 12PM. The arrival rate increases linearly from eight per hour at 12PM to twelve per hour at 3PM. The arrival rate drops linearly from twelve per hour at 3PM to four per hour at 6PM. The clinic stops taking in patients at 6PM. (a) What is the probability distribution of the number of patients that enter the clinic on a given day? You should write down correct parameter for the probability distribution. (b) Given that 5 patients arrived in the first 2 hours after the clinic opened, what is the probability that at least 1 patient arrives in the next hour?
7. A clinic opens at 7 AM. Patients arrive at a Poisson rate of five an hour from 7AM until 10AM. They arrive at a Poisson rate of eight an hour between 10AM and 12PM. The arrival rate increases linearly from eight per hour at 12PM to twelve per hour at 3PM. The arrival rate drops linearly from twelve per hour at 3PM to four per hour at 6PM. The clinic stops taking in patients at 6PM. (a) What is the probability distribution of the number of patients that enter the clinic on a given day? You should write down correct parameter for the probability distribution. (b) Given that 5 patients arrived in the first 2 hours after the clinic opened, what is the probability that at least 1 patient arrives in the next hour?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Transcribed Image Text:7. A clinic opens at 7 AM. Patients arrive at a Poisson rate of five an hour from 7AM
until 10AM. They arrive at a Poisson rate of eight an hour between 10AM and 12PM.
The arrival rate increases linearly from eight per hour at 12PM to twelve per hour at
3PM. The arrival rate drops linearly from twelve per hour at 3PM to four per hour at
6PM. The clinic stops taking in patients at 6PM.
(a) What is the probability distribution of the number of patients that enter the clinic
on a given day? You should write down correct parameter for the probability
distribution.
(b) Given that 5 patients arrived in the first 2 hours after the clinic opened, what is
the probability that at least 1 patient arrives in the next hour?
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