STAT330 Study Guide - Quiz Guide: Maximum Likelihood Estimation, Delta Method, Independent And Identically Distributed Random Variables

• School: University of Waterloo
• Department: Statistics
• Course: STAT330
• Professor: Christine Dupont

Document Summary

Due: thursday, july 26, 2012 by 5pm in m3 3112: suppose x1, x2, . , xn are i. i. d. random variables with e(xi) = , v ar(xi) = Xi=1 (xi xn)2 be the sample mean and sample variance respectively. (a) show that. S2 n = n n 1 1 n n! i x 2. Xi=1 (b) using the wlln and slutsky"s theorem, show that s2 n (c) hence, using the clt and slutsky"s theorem, show that p. Z n(0, 1): suppose x1, x2, . , xn are i. i. d. with p. d. f. f (x; ) =( x. , x < 0 where > 0. (a) if x has pdf f (x; ), show that e(x) =p (b) show that the method of moment estimator of is. 2 , e(x 2) = 2 2, and e(x 4) = 8 4. Xn with xn = nxi=1: show that m m, find the limiting distribution of n( m m ).