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 . The probability that a patient comes with disease 1 is p, while the probability for disease 2 is 1p. 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?.