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Unformatted text preview: ECE 5510: Random Processes Lecture Notes Fall 2009 Lecture 3 Today: (1) Conditional Probability, (2) Trees, (3) Total Prob ability Announcements: 1. HW 1 due Thursday at 5pm. It is a short HW, don’t get behind. 2. Reading for today: Sections 1.5,1.7, Mlodinow handout. 3. Reading for Thursday: 1.81.9, and 2.12.4. 1 Conditional Probability Example: Three Card Monte (Credited to Prof. Andrew Yagle, U. of Michigan.) There are three twosided cards: red/red, red/yellow, yellow/yellow. The cards are mixed up and shuffled, one is selected at random, and you look at one side of that card. You see red. What is the prob ability that the other side is red? Three possible lines of reasoning on this: 1. Bottom card is red only if you chose the red/red card: P = 1 / 3. 2. You didn’t pick the yellow/yellow card, so either the red/red card or the red/yellow card: P = 1 / 2. 3. There are five sides which we can’t see, two red and three yellow: P = 2 / 5. Which is correct? Def’n: Conditional Probability, P [ A  B ] P [event A occurs, GIVEN THAT event B occurred] For events A and B , when P [ B ] > 0, P [ A  B ] defines P [ A ∩ B ] P [ B ] = P [ A ∩ B ] P [ A ∩ B ] + P [ A c ∩ B ] Notes: ECE 5510 Fall 2009 2 1. Given that B occurs, now we know that either A ∩ B occurs, or A c ∩ B occurs. 2. We’re defining a new probability model, knowing more about the world. Instead of P [ · ], we call this model P [ · B ]. All of our Axioms STILL APPLY!...
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This note was uploaded on 09/15/2011 for the course ECE 5510 taught by Professor Chen,r during the Fall '08 term at Utah.
 Fall '08
 Chen,R

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