homework7

homework7 - =-β 1 1 b Find E[K and Var(K using iterated...

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C OMER ECE 600 Homework 7 1. A message requires N time units to be transmitted, where N is a geometric random variable with pmf p j = (1-a)a j-1 for j=1, 2,…. A single new message arrives during a time unit with probability p, and no new messages arrive with probability 1-p. Let K be the number of new messages that arrive during the transmission of a single message. a. Find the pmf of K. Hint : k n k n k k n - = + - ± ± ² ³ ´ ´ µ
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Unformatted text preview: ¶ =-β ) 1 ( ) 1 ( . b. Find E[K] and Var(K) using iterated expectation. 2. For any two random variables X and Y with E[X 2 ] < & , show that Var(X) ± E[Var(X|Y)], where Var(X|Y) = E[X 2 |Y] – (E[X|Y]) 2 . 3. Let X and Y be independent random variables with variances ² X 2 and ² Y 2 . Consider the sum Y ) 1 ( X Z a a-+ = where 0 ³ a ³ 1. Find a that minimizes the variance of Z....
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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.

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