1. 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
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
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
Probability & Stochastic Processes
Yates & Goodman (2nd Edition) NTUEE SCC_04_2008

5. 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

6. Correlation Example 6

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

17. 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)=

32. 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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