Problem 5.19 The “placebo effect” refers to treatment where a substantial proportion of the patients report a significant improvement even though the treatment consists of nothing more than giving the patient a sugar pill or some other harmless inert substance. Ten patients are given a new treatment for symptoms of a cold. The patients’ reactions fall into one of three categories: helped, harmed, and no effect. From previous experience with placebos it is known that P(helped)=0.50, P(harmed)=0.30, and P(no effect)=0.20. Let Y1, Y2, Y3 denote the number of patients in each of the three categories (helped, harmed, no effect). Assuming that the new treatment is no more effective than a placebo compute:

(a) E(Yi), i = 1, 2, 3.

(b) P(Y1 = 5, Y2 = 3, Y3 = 2).