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Problem 1 In a hospital, patients get treated for two different diseases, labelled 1 and 2. Each patient is independently treated such that the time to get fully treated and leave the hospital is exponential with parameter r₁ for disease 1 and r2 for disease 2. a. When k₁ patients start treatment for disease 1 and k2 patients for disease 2, what is the probability that the first patient to leave was treated for disease 1? On average, what is the first time a patient leaves? b. Patients arrive to the hospital as a Poisson process with rate A. The probability that a patient comes with disease 1 is p, while the probability for disease 2 is 1 - p. Patients start treatment as they arrive. By time t > 0, what is the average number of patients who have been fully treated for disease 1? What is the average number of patients who have been fully treated in total?

Problem 1 In a hospital, patients get treated for two different diseases, labelled 1 and 2. Each patient is independently treated such that the time to get fully treated and leave the hospital is exponential with parameter r₁ for disease 1 and r2 for disease 2. a. When k₁ patients start treatment for disease 1 and k2 patients for disease 2, what is the probability that the first patient to leave was treated for disease 1? On average, what is the first time a patient leaves? b. Patients arrive to the hospital as a Poisson process with rate A. The probability that a patient comes with disease 1 is p, while the probability for disease 2 is 1 - p. Patients start treatment as they arrive. By time t > 0, what is the average number of patients who have been fully treated for disease 1? What is the average number of patients who have been fully treated in total?

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter1: Equations And Graphs
Section: Chapter Questions
Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...
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Problem 1 In a hospital, patients get treated for two different diseases, labelled 1 and 2. Each patient is independently treated such that the time to get fully treated and leave the hospital is exponential with parameter r₁ for disease 1 and r2 for disease 2. a. When k₁ patients start treatment for disease 1 and k2 patients for disease 2, what is the probability that the first patient to leave was treated for disease 1? On average, what is the first time a patient leaves? b. Patients arrive to the hospital as a Poisson process with rate A. The probability that a patient comes with disease 1 is p, while the probability for disease 2 is 1-p. Patients start treatment as they arrive. By time t > 0, what is the average number of patients who have been fully treated for disease 1? What is the average number of patients who have been fully treated in total?
Transcribed Image Text:Problem 1 In a hospital, patients get treated for two different diseases, labelled 1 and 2. Each patient is independently treated such that the time to get fully treated and leave the hospital is exponential with parameter r₁ for disease 1 and r2 for disease 2. a. When k₁ patients start treatment for disease 1 and k2 patients for disease 2, what is the probability that the first patient to leave was treated for disease 1? On average, what is the first time a patient leaves? b. Patients arrive to the hospital as a Poisson process with rate A. The probability that a patient comes with disease 1 is p, while the probability for disease 2 is 1-p. Patients start treatment as they arrive. By time t > 0, what is the average number of patients who have been fully treated for disease 1? What is the average number of patients who have been fully treated in total?
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