Homework1sol.pdf - IEOR-E4707 Spring 2018 Homework 1...

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IEOR-E4707, Spring 2018: Homework 1 Solutions January 24, 2018 Problem 1. Consider a general random walk S n = X 1 + ... + X n , where X i ’s are i.i.d with mean μ and variance σ 2 . Show that ( S n - ) 2 - 2 is an F X n -martingale.
Problem 2. Let X be an integrable random variable (i.e E [ X ] < ) and define X n = E [ X | F n ] , n = 0 , 1 , 2 , ... . Prove that { X n } n 0 is a martingale.

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