Patients at an emergency room are categorized into m types. Assume the arrivals of the m types of patients occur at times that form independent homogeneous Poisson processes with respective rates λ 1...

Patients at an emergency room are categorized into m types. Assume the arrivals of the m types of patients occur at times that form independent homogeneous Poisson processes with respective rates λ₁,...,λ_m. (a) Find the probability that a type 1 patient arrives before a type 2 patient. (b) What is the probability that the next patient to arrive after a specified time is of type 1? (c) Find the probability that in the next 5 arrivals, there are exactly 3 type 1 patients. (d) Find the probability that 3 type 1 patients arrive before the first type 2 patient. (e) Find the probability that the next patient to arrive is of type 1, 2 or 3.