hw6 - UCSD ECE 153 Handout #20 Prof. Young-Han Kim...

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

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: UCSD ECE 153 Handout #20 Prof. Young-Han Kim Thursday, November 20, 2008 Homework Set #6 Due: Thursday, December 4, 2008 1. Read Sections 7.1–7.4, 9.1–9.6, 10.1–10.2, 10.4 in the text. Try to work on all examples. 2. Symmetric random walk. Let X n be a random walk defined as X = 0 X n = n summationdisplay i =1 Z i , where Z 1 ,Z 2 ,... are i.i.d. with P( Z 1 =- 1) = P( Z 1 = 1) = 1 2 . (a) Find P { X 10 = 10 } . (b) Find P { max 1 ≤ i< 20 X i = 10 | X 20 = 0 } . (c) Find P { X n = k } . 3. Moving average process. Let Y n = 1 2 Z n- 1 + Z n for n ≥ 1 , where Z ,Z 1 ,Z 2 ,... are i.i.d. ∼ N (0 , 1). Find the mean and autocorrelation function of Y n . 4. Gauss-Markov process. Let X = 0 and X n = 1 2 X n- 1 + Z n for n ≥ 1, where Z 1 ,Z 2 ,... are i.i.d. ∼ N (0 , 1). Find the mean and autocorrelation function of X n . 5. Discrete-time Wiener process. Let Z n , n ≥ 0 be a discrete time white Gaussian noise (WGN) process, i.e., Z 1 ,Z 2 ,... are i.i.d. ∼ N (0 , 1). Define the process1)....
View Full Document

This note was uploaded on 10/26/2011 for the course MATH 180C taught by Professor Eggers during the Winter '09 term at Aarhus Universitet.

Page1 / 2

hw6 - UCSD ECE 153 Handout #20 Prof. Young-Han Kim...

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

View Full Document Right Arrow Icon
Ask a homework question - tutors are online