Question

a) A clinic is staffed by two physicians who worked sequentially. The first works from time 0 to time t1, and the second works from time t1 to time t2 independently of the first. Patients arrive at the clinic following a Poisson distribution with parameter lambda per unit time. Given the total number of patients seen in the time interval (0, t2) is n, find the probability distribution of the total number of patients seen by physician 1.

b) Clinical trials identify patients through a series of sequential mechanisms. The first step is to select patients from the general population who are interested and might be participants in the study, producing a “screened population”. The second step is to make sure each patient in the screened population is eligible for the study by meeting all of the study’s inclusion and exclusion criteria; this generates an “eligible population”. The third step is to obtain an informed consent from the patient and randomize them to a study medication, creating a “randomized population”. All randomized patients are eligible and screened. All eligible patients are screened.

Examine the data below (Table 1) and answer the following questions.

Table 1 Demographics of Screened, Eligible, and Randomized Patients

                        Screened         Eligible             Randomized

Total               300                  140                  100

Race

NonWhite       50                    30                    25

White              250                  110                  75

Ethnicity

Hispanic          100                  40                    3

NonHispanic 200                  100                  97

Find the probabilities of the subsequent events:

a) A screened patient is eligible.

b) An eligible patient is randomized.

c) 30 nonwhites and 110 nonwhites would be selected from screened population for the eligible population of 140.

d) A Hispanic patient is a member of the randomized population.

Please reference formulas or theorems used to solve the problem.

Answer 1