Question 1 Data Generation Use a linear congruential generator with parameters a = 41, c = 33, m = 100 and Z0 = 48 to generate a series of 100 numbers uniformly distributed in the interval [0,1]. a) Compute and compare the mean and standard deviation of these numbers with those obtained from the expected theoretical Uniform(0,1) distribution (continuous uniform). Explain any differences. b) A rheumatology clinic at a large teaching hospital in Ontario classifies patients into five priority classes with maximum clinically recommended wait times of 2, 9, 13, 26 and 52 weeks, respectively. The clinic observes weekly service requests with rates of 0.78, 7.41, 13.26, 10.05 and 7.50 for patients of priority 1, 2, 3, 4 and 5, respectively. Using this information and the uniform random numbers from part a), generate 100 observations for the priority of the patient associated with a randomly arriving service request to the rheumatology clinic.