131A_1_ds2_2010fall_Sol

131A_1_ds2_2010fall_Sol - EE 131A Probability Instructor...

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Discussion Set 2 Probability Wednesday, October 6, 2010 Instructor: Lara Dolecek and Friday, October 8, 2010 Reading: Chapter 2 of Probability, Statistics, and Random Processes by A. Leon-Garcia 1. Conditional Probability. Problem 2.73, page 88 of ALG (a) If P ( A B ) = 0, then P ( A | B ) = P ( A B ) P ( B ) = 0 If P ( A B ) = 0, then P ( A | B ) = P ( A B ) P ( B ) = P ( A ) P ( B ) If P ( A B ) = 0, then P ( A | B ) = P ( A B ) P ( B ) = P ( B ) P ( B ) = 1 (b) If P ( A | B ) > P ( A ), then P ( A | B ) = P ( A B ) P ( B ) > P ( A ) P ( B ) < P ( A B ) P ( A ) = P ( B | A ) 2. Binary Communication and Malicious Interferer . Problem 2.4, page 81 of ALG (a) S = { 2 , 1 , 0 , - 1 , - 2 } (b) T = { 2 , 1 } . Note that T does NOT include 0. (c) The two tosses of the coin being both heads will result in the outcome of Y = 0. Problem 2.78, page 89 of ALG (a) The tree diagram is shown as the following: 1/2 1/2 1/2 1/2 1/4 1/4 1/4 1/4 +2 -2 +2 +1
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This note was uploaded on 02/03/2011 for the course EE 131A taught by Professor Lorenzelli during the Fall '08 term at UCLA.

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131A_1_ds2_2010fall_Sol - EE 131A Probability Instructor...

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