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ECEN4503 Random Signals Lecture # 4 22 January 2014 Dr. George Scheets

ECEN4503 Random Signals Lecture # 4 22 January 2014 Dr. George Scheets. Read Chapter 2.7-3.1 Homework: Chapter 2: 20, 22, 25, & 26 (1 st Edition) Homework: Chapter 2: 51, 53, 58, 59 (2 nd Edition) Quiz #1 on 24 January. Quiz #1 Next Time. Covers Chapter 2 (text)

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ECEN4503 Random Signals Lecture # 4 22 January 2014 Dr. George Scheets

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  1. ECEN4503 Random SignalsLecture #4 22 January 2014Dr. George Scheets • Read Chapter 2.7-3.1 • Homework: Chapter 2: 20, 22, 25, & 26 (1st Edition) • Homework: Chapter 2: 51, 53, 58, 59 (2nd Edition) • Quiz #1 on 24 January

  2. Quiz #1 Next Time • Covers Chapter 2 (text) • < Random Variables (notes) • Open Book, Notes, Instructor, & TA • Closed Neighbor • For All Quizzes & Tests... • Calculators allowed • So long as I/O only keyboard & screen • Smart Phones are NOT allowed

  3. Probability • Bounded by [0,1] • P(A + B) = P(A) + P(B) - P(AB) • P(a|b) = P(ab)/P(b) (Conditional Probability) • P(ab) = P(a)P(b) (Statistically Independent) • P(b) = P(a1b) + ... + P(anb) (Total Probability) • P( a1 + ...+ an ) must = 1ai∩ aj must be mutually exclusive, i ≠ j • P(a|b)P(b) = P(b|a)P(a) = P(ab) (Baye's Theorem)

  4. Bernoulli Trials & Binomial Distribution • You must have a two state experiment • Success or Failure • Stable probabilities • You must be interested in the number of successes (or failures) • Specific order not important • The individual experiments must be Statistically Independent

  5. Need P(Number of Outcomes)? • 1) Bernoulli Trial? Yes? Binomial Dist. • 2) If no, think Conditional Probability • Draw an event tree • Assign probabilities P(b1|a1) P(a1∩b1) P(a1) P(b2|a1) P(a1∩b2) P(b3|a2) P(a2∩b3) P(a2) P(a2∩b4) P(b4|a2) P(b5|a3) P(a3) P(a3∩b5) P(b6|a3) P(a3∩b6)

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