Suppose that the time, T, from treatment to a recurrence for patients diagnosed with a disease is assumed to follow an Exponential distribution with a mean, 3 = 800 days. a. What is the probability that a patient will make it through 520 days without a recurrence? b. If it has been 520 days since a patient has received treatment, without a recurrence, what is the probability that the patient will make it through the next 520 days without a recurrence? What property is being demonstrated here? c. The data below give a data summary on the recurrence times for 80 patients who were treated for the disease. The average recurrence time for this sample of patients is f = 800. If the times are assumed to be independent from patient to patient, and the data are assumed to follow an exponential distribution with mean 3 = 800 days, give an expression for the probability of observing the data given in the table below. Notes: A square bracket, or "]\" implies that the value i_s included in the interval. A round bracket, or \"[\" implies that the value is not included in the interval. An expression is ne here. There is no need to compute an actual numerical answer. Time to Recurrence Da 5 0, 4-00 400, 800 800, 1200 _ 1200, 1600 > 1600 Number of Patients \"-_