STAT330 Lecture : Lecture_July3rd.pdf

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

Document Summary

Let x1, x2, , xn be i. i. d r. v. s with e(xi) = and. A useful result for proving central limit theorem. Let x1, x2, , xn, be a se- quence of r. v. s such that xn has m. g. f mn(t) and let x be a r. v. with m. g. f m(t). If there exists an h > 0 such that for all t ( h, h) then xn d x. , xn are iid random variables from 2. Let yn = pn limiting distribution of (yn n )/ n . i=1 xi. Suppose x1, x2, , xn are i. i. d p oi( ) r. v. s. Find the limiting distribution of zn = n( xn )/q xn and un = n( xn ). Suppose x1, , xn is a random sample from the exp ( ) distribution. Find the limiting distribution of (a) xn, (b) zn = n( xn )/ xn, (c) un = n( xn ).