hw2 - EE 378 Handout#8 Statistical Signal Processing...

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Unformatted text preview: EE 378 Handout #8 Statistical Signal Processing Wednesday, April 18, 2007 Homework Set #2 Due: Wednesday, April 25, 2007. Announcement: You can hand in the HW either after class or deposit it, before 5pm, in the Homework in box in the 378 drawer of the class file cabinet on the second floor of the Packard Building. 1. Using the definitions given in class, show that the following are martingales (a) Z n = ∑ n i =1 X i , where X i are iid random variables with zero mean. (b) Z n = Q n i =1 X i , where X i are iid random variables with mean one. 2. Using the definitions given in class, show that (a) If a set of random variables V 1 , V 2 , ... is a martingale difference sequence w.r.t. X 1 , X 2 , ... , then V 1 , V 2 , ... is a martingale difference sequence (w.r.t. itself). (b) If Z 1 , Z 2 , ... is a martingale, then V i , Z i- Z i- 1 is a martingale difference. Con- versely, if V 1 , V 2 , ... is a martingale difference, then Z i , ∑ i j =0 V j is a martingale....
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hw2 - EE 378 Handout#8 Statistical Signal Processing...

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