ECEN4503 Random SignalsECEN4503 Random SignalsLecture #1 & 2; 13 & 15 January 2014Lecture #1 & 2; 13 & 15 January 2014ECEN4503 Random SignalsECEN4503 Random SignalsLecture #1 & 2; 13 & 15 January 2014Lecture #1 & 2; 13 & 15 January 2014

Read Chapter 1Read Chapter 1 Read Sections 2.1 - 2.3Read Sections 2.1 - 2.3 Problems 2.3, 2.8, 2.9, 2.10 (1Problems 2.3, 2.8, 2.9, 2.10 (1STST edition) edition) Problems 2.9, 2.16, 2.23, 2.24 (2Problems 2.9, 2.16, 2.23, 2.24 (2ndnd edition) edition) Quiz #1 on 24 JanuaryQuiz #1 on 24 January

ECEN4503 Random SignalsECEN4503 Random SignalsLecture #3 17 January 2014Lecture #3 17 January 2014Dr. George ScheetsDr. George Scheets

ECEN4503 Random SignalsECEN4503 Random SignalsLecture #3 17 January 2014Lecture #3 17 January 2014Dr. George ScheetsDr. George Scheets

Read sections 2.4 - 2.6Read sections 2.4 - 2.6 Homework: 2.11, 2.13, 2.15, 2.16 (1Homework: 2.11, 2.13, 2.15, 2.16 (1stst Edition) Edition) Homework: 2.35, 2.39, 2.26, 2.45 (2Homework: 2.35, 2.39, 2.26, 2.45 (2ndnd Edition) Edition) Quiz #1 on 24 JanuaryQuiz #1 on 24 January

GradingGrading In Class: Quizzes, Tests, Final ExamIn Class: Quizzes, Tests, Final Exam

Open Book & Open NotesOpen Book & Open NotesWARNING! WARNING! Study for them like they’re closed book!Study for them like they’re closed book!

Ungraded Homework: Ungraded Homework: Assigned most every classAssigned most every classNot collectedNot collectedSolutions ProvidedSolutions ProvidedPayoff: Tests & QuizzesPayoff: Tests & Quizzes

Why work the ungraded Homework problems?Why work the ungraded Homework problems?

An Analogy: Data Com vs. SoccerAn Analogy: Data Com vs. Soccer Reading text = Reading a book about SoccerReading text = Reading a book about Soccer Looking at the problem solutions = Looking at the problem solutions =

watching a scrimmage watching a scrimmage WorkingWorking the problems = the problems =

practicing or playing in a scrimmage practicing or playing in a scrimmage Quiz = Exhibition GameQuiz = Exhibition Game Test = Big GameTest = Big Game

To succeed in this class...To succeed in this class...

Show some self-discipline!! Important!!Show some self-discipline!! Important!!For every hour of class...For every hour of class...

... put in 1-2 hours of your own effort.... put in 1-2 hours of your own effort.

PROFESSOR'S LAMENTPROFESSOR'S LAMENTIf you put in the timeIf you put in the timeYou should do fine.You should do fine.If you don't,If you don't,You likely won't.You likely won't.

CheatingCheating Don’t do it!Don’t do it!

If caught, expect to get an ‘F!’ for the course.If caught, expect to get an ‘F!’ for the course.

My idol:My idol:Judge Isaac ParkerJudge Isaac ParkerU.S. Court: Western District of ArkansasU.S. Court: Western District of Arkansas1875-18961875-1896

a.k.a. “Hanging Judge Parker”a.k.a. “Hanging Judge Parker”

Why is 4503 Required?Why is 4503 Required? Controls, Communications, IC DesignControls, Communications, IC Design

Random, unpredictable, signalsRandom, unpredictable, signals What voltages are most likely?What voltages are most likely? What frequencies are most likely?What frequencies are most likely?

Another Field?Another Field? May help you at VegasMay help you at Vegas

Important EnoughImportant Enough ABET Requires it for accreditationABET Requires it for accreditation

ProbabilityProbability

Is a number between 0 and 1, inclusiveIs a number between 0 and 1, inclusive

Quiz or test answer outside this range?Quiz or test answer outside this range? After 1st test, note something is not right!!!After 1st test, note something is not right!!! PENALTY WILL ESCALATE!!!PENALTY WILL ESCALATE!!!

Will max out at zero credit for problem on Will max out at zero credit for problem on Final Exam.Final Exam.

Define Your Events

Before Calculatinga

Probability

Define Your Events

Before Calculatinga

Probability

Probability of UnionsProbability of Unions

P(a + b) = P(a) + P(b) - P(ab)P(a + b) = P(a) + P(b) - P(ab) If ab = {null set}, a & b are If ab = {null set}, a & b are Mutually ExclusiveMutually Exclusive

In this case, clearly P(ab) = 0In this case, clearly P(ab) = 0

Use Venn Diagrams for more complicated Use Venn Diagrams for more complicated expressionsexpressions Such as P(a + b + c + d)Such as P(a + b + c + d) Insure each area is counted only onceInsure each area is counted only once

Other Key Theorems to KnowOther Key Theorems to Know

P(a)P(b|a) = P(ab)P(a)P(b|a) = P(ab) Conditional ProbabilityConditional Probability

P(ab) = P(a)P(b)P(ab) = P(a)P(b) iff a and b are Statistically Independentiff a and b are Statistically Independent

P(b) = P(aP(b) = P(a11b) + ... + P(ab) + ... + P(annb)b) Total ProbabilityTotal Probability

P( aP( a11 + ...+ a + ...+ an n ) must = 1) must = 1

aaii ∩ a∩ ajj must be mutually exclusive, i ≠ j must be mutually exclusive, i ≠ j

7) P(a|b)P(b) = P(b|a)P(a) 7) P(a|b)P(b) = P(b|a)P(a) = P(ab) = P(ba)= P(ab) = P(ba) Baye's TheoremBaye's Theorem