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Random Vectors: Functions of R.Vs & Conditional PDF

Explore concepts like bivariate R.Vs, probability models, and vector notation in Lecture 12. Learn about expected values, correlation matrices, and Gaussian random vectors with practical examples and readings.

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Random Vectors: Functions of R.Vs & Conditional PDF

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  1. Lecture 12Vector of Random Variables Last Time (5/7) Pairs of R.Vs. Functions of Two R.Vs Expected Values Conditional PDF Reading Assignment: Sections 4.6-4.9 Probability & Stochastic Processes Yates & Goodman (2nd Edition) NTUEE SCC_05_2008

  2. Makeup Classes I will attend Networking 2009 in Aachen, Germany, and need to make-up the classes of 5/14 & 5/15 (3 hours) • 5/7 17:30 – 18:20, 5/8 8:10 – 9:00 • 5/21 17:30 – 18:20, Probability & Stochastic Processes Yates & Goodman (2nd Edition) NTUEE SCC_05_2008

  3. Lecture 12: Random Vectors Today (5/8) • Independence between Two R.Vs • Bivariate R.V.s • Random Vector • Probability Models of N Random Variables • Vector Notation • Marginal Probability Functions • Independence of R.Vs and Random Vectors • Function of Random Vectors Reading Assignment: Sections 4.10-5.5 Probability & Stochastic Processes Yates & Goodman (2nd Edition) NTUEE SCC_05_2008

  4. Lecture 12: Random Vector Next Time: • Random Vectors • Function of Random Vectors • Expected Value Vector and Correlation Matrix • Gaussian Random Vectors • Sums of R. V.s • Expected Values of Sums • PDF of the Sum of Two R.V.s • Moment Generating Functions Reading Assignment: Sections 5.5-6.3 Probability & Stochastic Processes Yates & Goodman (2nd Edition) NTUEE SCC_04_2008

  5. Correlation of Wafer Acceptance Test (WAT) and In-line Manufacturing Process ….. Inline n Inline 1 Inline 2 Inline 3 WAT 5 • Objective • Analyze and monitor sensitivity of WAT parameter to In-line then keep WAT unchanged by adjusting In-line shift. • Multiple Regression Model (MRM)

  6. Correlation Example 6

  7. Brain Teaser: If You Were Kalman … 12 - 7

  8. • Example: Let the number of men and women entering a post office in a certain interval be two independent Poisson random variables with parameters l and m , respectively. Find the conditional probability function of the number of men given the total number of persons. Solution: Let N, M, K be the total number of men, women, and persons entering the post office. Note that K = M+N and M, N are independent. So we have K is also Poisson with parameter l+m. pN|K(n|k) = P(N=n)P(M=k-n)/P(K=k)= 12 - 17

  9. Probability and Stochastic ProcessesA Friendly Introduction for Electrical and Computer EngineersSECOND EDITIONRoy D. Yates David J. Goodman Definitions, Theorems, Proofs, Examples, Quizzes, Problems, Solutions Chapter 5

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