1. (35pts) Let X1, ... X, be a random sample from a distribution with pdf given as Or#-1 0

1. (35pts) Let Xl, ... Xn be a random sample from a distribution with pdf given as Oxol, O < x < 1 {0 One can show that E(Xi) and VT(S) otherwise 9 (0+1) (0+2) (a) (15pts) Find the method of moments estimator of 0. (b) (20pts) Find the maximum likelihood estimator of 0.