2. Let X1, X2, ..., X, be independent random variables with density f(I; 0) - AY where y is a known constant and 0 > 0 is an unknown parameter. a) Prove that the density of (X1, X2, . .., X.) has a monotone likelihood ratio in the statistic Z = X(m) = max(X1, X2, . . ., X,.). b) Find the cumulative distribution function and the density of the statistic Z - X (n). c) Find the uniformly most powerful a-size test o* of Ho : 0