Patients arrive to an emergency hospital unit according to a Poisson process with parameter > > 0. They are assisted on a first arrived first assisted basis. Patients are assisted one by one. a) Estimate the parameter 2 based on the data in the table below. Each observation represents the number of daily patients arrived to the emergency hospital.b) Find the probability that no arrivals occur in an interval of 5 hours. c) Find the probability that at least one arrival occurs in a day. (1) What is the estimated mean and the variance of the number of arrivals during a day? e) The time a single patient takes to be completely assisted has a random probability distribution with exponential distribution of parameter p = 30 min/patient. Find the average and the standard deviation of the total time patients have been assisted during a day. Find the p.d.f. of the total time