Problem 1: Poisson Probabilities You are involved in a major patient recruiting effort in a clinical trial to reduce the incidence of death following acute myocardial infarction (AMI). Patients are being recruited in each of 7 clinical centers. Once recruited, these patients will then be randomly assigned either active medication and placebo and followed for an average of six months. Assume the probability that k patients are randomized by a given center is Poisson with parameter lambda = 0.3 patients per week. Find the following probabilities. The probability a given center recruits 1 patient this week. The probability a given center randomizes 2 or fewer patients this week The probability a given center randomizes at least 1 patient this week . The probability that in five of the next seven weeks, a given center randomizes at least one patient a week in each of those five weeks. The probability that the total number of patients randomized by all seven centers is at least 4 this week (you can provide an exact solution, or you may use the F11 DOW