Lecture 12 Vector of Random Variables

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Presentation transcript:

Lecture 12 Vector 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

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

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

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

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

Correlation Example 6

Brain Teaser: If You Were Kalman … 12 - 7

pN|K(n|k) = P(N=n)P(M=k-n)/P(K=k)= • 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

Definitions, Theorems, Proofs, Examples, Quizzes, Problems, Solutions Probability and Stochastic Processes A Friendly Introduction for Electrical and Computer Engineers SECOND EDITION Roy D. Yates David J. Goodman Definitions, Theorems, Proofs, Examples, Quizzes, Problems, Solutions Chapter 5

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