How tom solve the question (c) and (e) Let Y1,Y2,,Yn denote a random sample of size n from a population with a uniform distribution on the interval (0,). Let Y(n)=max(Y1,Y2,,Yn) and U=(1/)Y(n). a Show that U has distribution function FU(u)=0,un,1,u<00u1u>1. b Because the distribution of U does not depend on ,U is a pivotal quantity. Find a 95% lower confidence bound for . (c) Check if U is a pivotal quantity. (d) Find the cdf of U. (e) Find a 95% confidence interval for . i. Find a and b such that P(aUb)=P(aY(n)/b)=0.95 Hint : Use the cdf of U in (d). For example, solve P(U b)=0.975 for b ii. Rearrange the interval aY(n )/b in terms of ..