8. The proportion of rats that successfully complete a designed experiment (e.g., running through a maze)...
8. The proportion of rats that successfully complete a designed experiment (e.g., running through a maze) is of interest for psychologists. Denote by Y the proportion of rats that complete the experiment, and suppose that the experiment is replicated in 10 different rooms. Assume that Yı,Y2,...,Y10 are independent and identically distributed (iid) beta random variables with a = 2 and B = 1. (a) Find the pdf of Yn), the largest order statistic. Note: The resulting pdf should be a beta pdf (b) Find P(Y(1) > 0.90). (c) Find E(Y(n)).