Unformatted text preview: < p < 1 / 2. Let S n = Y 1 + Â· Â· Â· + Y n denote their partial sums. (a) Show that X n = S nn (2 p1) is a martingale (b) Show that Z n = Â± 1p p Â² S n is a martingale 2. Consider the following sequence X ,X 1 ,X 2 ,. .. of random variables. Suppose that p, q âˆˆ (0 , 1) and set X = p . Suppose further that the distribution of X n +1 depends only on X n by P ( X n +1 = (1q ) X n  X n ) = 1X n , P ( X n +1 = q + (1q ) X n  X n ) = X n . Show that { X n , n = 0 , 1 ,. .. } is a martingale....
View
Full
Document
This note was uploaded on 03/26/2012 for the course STAT 351 taught by Professor Michaelkozdron during the Fall '08 term at University of Regina.
 Fall '08
 MichaelKozdron
 Probability

Click to edit the document details