homework6 - C OMER ECE 600 Homework 6 1. Show that if X is...

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Unformatted text preview: C OMER ECE 600 Homework 6 1. Show that if X is a Cauchy random variable with parameter & , then - = e ) ( X where X ( ) = E[e j x ] is the characteristic function of X. 2. Let X be a random variable with characteristic function X ( ). Show that | X ( )| takes on its maximum value at = 0. 3. The number of bytes N in a message has a geometric distribution with parameter p , i.e., ,... 3 , 2 , 1 , , ) 1 ( ) ( p N =- = k p p k k where 0 p 1. (Note that this is an alternate version of the geometric pmf, and is slightly different from that presented in class). Suppose that messages are broken into packets of length M bytes. Let Q be the number of full packets in a message and let R be the number of bytes left over. Find the joint pmf and the marginal pmfs of Q and R. Are Q and R independent? 4. Let X and Y be continuous random variables and cos Y sin X W sin Y cos X Z +- = + = where the angle is non-random. Find f ZW in terms of f...
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This note was uploaded on 01/27/2010 for the course ECE 600 taught by Professor Staff during the Fall '08 term at Purdue University-West Lafayette.

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homework6 - C OMER ECE 600 Homework 6 1. Show that if X is...

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