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

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

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

## This note was uploaded on 03/03/2011 for the course EE 378 taught by Professor Weissman,i during the Spring '07 term at Stanford.

### Page1 / 3

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

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

View Full Document
Ask a homework question - tutors are online