12. 19 a clinical study of a new drug formulated to reduce the effects of rheumatoid arthritis, researchers found that the proportion P of patients: who respond favorably to the drug is a random variable that varies from batch to batch of the drug. Assume that P has density function f (p) = 12p2(1 p), < p < -i. Suppose that n patients are injected with portions of the drug taken from the same batch. Let V denote the number showing a favorable response, Find (a) the unconditional probability function p(y) for a general and '(b) E(Y) for n 2. 12 Ans. (a) p(y)