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Unformatted text preview: < p < 1 / 2. Let S n = Y 1 + + Y n denote their partial sums. (a) Show that X n = S nn (2 p1) is a martingale (b) Show that Z n = 1p p S n is a martingale 2. Consider the following sequence X ,X 1 ,X 2 ,. .. of random variables. Suppose that p, q (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....
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 Fall '08
 MichaelKozdron
 Probability

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