ps10 - ECSE-305, Winter 2009 Probability and Random Signals...

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Unformatted text preview: ECSE-305, Winter 2009 Probability and Random Signals I Assignment #10 Posted: Thursday, April 2, 2009. Due: Tuesday, April 14, 2009, 11h00am, MC756. Notes: Assignments without this cover page will be discarded. Student #1: Name: ID: Student #2: Name: ID: Question Marks 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Total 1. Let X 1 , X 2 , . . . be independent and identically distributed (i.i.d.) ran- dom variables with P ( X n = 1) = p and P ( X n =- 1) = q = 1- p , for all n . Define Y n = n summationdisplay i =1 X i n = 1 , 2 , . . . and Y = 0. The collection of RVs { Y n : n } is a random process, called a random walk . (a) What type of process is Y n ? Identify the index parameter T and the state space . (b) Construct a typical realization of Y n in the case p = 1 / 2. (Hint: use a coin...) (c) Find the mean and variance function, i.e. Y ( n ) and 2 Y ( n ), of the process Y n . 2. Consider a random process X ( t ) defined by X ( t ) = A sin(2 Ft ) , t where the amplitude A is a discrete RV with...
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This note was uploaded on 09/30/2009 for the course ECSE 305 taught by Professor Champagne during the Spring '09 term at McGill.

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ps10 - ECSE-305, Winter 2009 Probability and Random Signals...

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