assignment8

assignment8 - 1 } ( x 1 ) . (k) Let Y 1 = X 1 + X 2 Y 2 = X...

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EE 505 B Fall 2011 Assignment 8 For full credit, you must show all of the steps or reasoning that you used to get the answer. 1. A joint probability density function is given as f X 1 X 2 ( x 1 , x 2 ) = b ce - x 1 x 1 > 0 and | x 2 | < x 1 0 otherwise (a) Draw the region for which the joint probability density function is non-zero. (b) Determine the value of c . (c) Find and sketch the marginal probability density functions. (d) Find the joint cumulative distribution function. (e) Evaluate Pr ( X 1 1 ) . (f) Evaluate Pr ( X 1 + X 2 < 1 ) . (g) Evaluate E { X 1 X 2 } . (h) Are X 1 and X 2 independent? Make sure that you justify your answer. (i) Find and sketch f X 1 | X 2 ( x 1 ) and f X 2 | X 1 ( x 2 ) . (j) Find and sketch f X 1 |{ X 2 >
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Unformatted text preview: 1 } ( x 1 ) . (k) Let Y 1 = X 1 + X 2 Y 2 = X 1-X 2 Find an expression for the joint probability density function for Y 1 and Y 2 . Are Y 1 and Y 2 independent? 2. The probability that the ±rst packet arrives at a certain network node at a time X given that the node comes online at a time Y is f X | Y ( x ) = b e-( x-y ) ≤ y ≤ x < ∞ x < y The probability that the node comes online at time Y is uniformly distributed be-tween 0 and 1. (a) Find the joint probability density function f XY ( x , y ) . (b) Find f X ( x ) . 1...
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This note was uploaded on 03/01/2012 for the course EE 101 taught by Professor Munk during the Spring '12 term at Alaska Anch.

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