1. Let X be a continous random variable with pdf f(a:;9) = axe92:2\

I. Let X be a continous random variable with pdf 9:c2 / 2 O) = Oxe O S a; < 00, where 0 is an unknown parameter with parameter space Q = {0 : 0 < 0 < 00}. Let Xl, ... be a random sample of X. a. Find the maximum likelihood estimator for 0 (b) Let Yl, ... , Yn be the order statistics for the random sample, and let a Find an expression for the probability P (Y2 < a < Y5). , xn