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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