20105ee131A_1_ps1_2010fall_Sol

# 20105ee131A_1_ps1_2010fall_Sol - EE 131A Probability...

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Problem Set 1 Probability Wednesday, September 29, 2010 Instructor: Lara Dolecek Due: Wednesday, October 6, 2010 Reading: Chapter 2 of Probability, Statistics, and Random Processes by A. Leon-Garcia 1. Dry pens. Problem 2.5, page 81 of ALG (a) Denote the good pens G Denote the dry pens B Then we have set S = { G,BG,BBG,BBBG,BBBBG } (b) The set S = { 1 , 2 , 3 , 4 , 5 } (c) The set S = { GG,GBG,GBBG,GBBBG,GBBBBG,BGG,BGBG,BGBBG, BGBBBG,BBGG,BBGBG,BBGBBG,BBBGG,BBBGBG,BBBBGG } (d) The set S = { 2 , 3 , 4 , 5 , 6 } 2. Equal sets. Problem 2.12, page 82 of ALG If A B = A , then B A . If A B = A , then A B . Therefore, if A B = A and A B = A , then A = B 3. Throwing dice. Problem 2.2, page 81 of ALG (a) S = { (1 , 1) , (1 , 2) , (1 , 3) , (1 , 4) , (1 , 5) , (1 , 6) (2 , 1) , (2 , 2) , (2 , 3) , (2 , 4) , (2 , 5) , (2 , 6) (3 , 1) , (3 , 2) , (3 , 3) , (3 , 4) , (3 , 5) , (3 , 6) (4 , 1) , (4 , 2) , (4 , 3) , (4 , 4) , (4 , 5) , (4 , 6) (5 , 1) , (5 , 2) , (5 , 3)

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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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20105ee131A_1_ps1_2010fall_Sol - EE 131A Probability...

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