03_26 - STAT 410 Examples for 03/26/2008 Spring 2008 Let...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Examples for 03/26/2008 Spring 2008 Let { X n } be a sequence of random variables and let X be a random variable. Let F X n and F X be, respectively, the c.d.f.s of X n and X. Let C ( F X ) denote the set of all points where F X is continuous. We say that X n converges in distribution to X if ( ) ( ) x x n n X X F F lim = , for all x C ( F X ). We denote this convergence by X X D n . Example 5 : Let X n have p.d.f. f n ( x ) = n n x 2 1 1 1 + + , for 0 < x < 1, zero elsewhere. Then X X D n , where X has a Uniform distribution over ( 0, 1 ). Example 6 : Let X have a Uniform distribution over ( 0, 1 ). Let P ( X n = n i ) = n 1 , for i = 1, 2, … , n . Note that X is continuous, while X n ’s are discrete. For 0 < x < 1, F X ( x ) = x , F X n ( x ) = n x n , where x ± = the greatest integer less than or equal to x . Therefore,
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/11/2011 for the course STAT 410 taught by Professor Monrad during the Spring '08 term at University of Illinois, Urbana Champaign.

Page1 / 4

03_26 - STAT 410 Examples for 03/26/2008 Spring 2008 Let...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online