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Lecture 10 Pairs of Random Variables Last Time Pairs of R.Vs. Joint CDF Joint PMF Marginal PMF Reading Assignment: Chapter 4.1 – 4.3 Probability & Stochastic Processes Yates & Goodman (2nd Edition) NTUEE SCC_04_2008 10 - 1

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Makeup Classes I will attend Networking 2009 in Aachen, Germany, and need to make-up the classes of 5/14 & 5/15 (3 hours) 4/30 17:30 – 18:20, 5/7 17:30 – 18:20, 5/8 8:10 – 9:00 Probability & Stochastic Processes Yates & Goodman (2nd Edition) NTUEE SCC_04_2008 10 - 2

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Lecture 10: Pair of R.V.s This Week Pairs of R.Vs. Marginal PMF (Cont.) Joint PDF Marginal PDF Functions of Two R.Vs Expected Values Conditioning by an Event Reading Assignment: Sections 4.3-4.11 Probability & Stochastic Processes Yates & Goodman (2nd Edition) NTUEE SCC_04_2008 10 - 3

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Lecture 10: Pairs of R.Vs Next Week: Random Vectors Probability Models of N Random Variables Vector Notation Marginal Probability Functions Independence of R.Vs and 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 5.1-6.3 Probability & Stochastic Processes Yates & Goodman (2nd Edition) NTUEE SCC_04_2008 10 - 4

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Brain Teaser Current level of influenza pandemic alert raised from phase 4 to 5 !! WHO 04/29/2009 Q1: What does the alert level mean? Q2: What is the probability that more than 10% of this class will be inffected? Challenge: Can you use probability theory, computer and statistical data from the web to estimate Prob(>10% of this class infected in 6 months)?

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Lessons from SARS Simulating SARS for Public Health Policy 孫春在 By Prof. 孫春在 (NTUEE79 系友 ) and his group Simulating SARS-short.ppt

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日光下並無新事 ( 傳道書一、 9-10) Smallpox: inoculation or not? - One urgent social issue in France from 1750 to 1770 - Over 10 percent London and Paris populations killed by Smallpox - Risky procedure using live smallpox pustules and could lead to death - Parisians’ choice: 1 in 7 longer-term chance of dying of smallpox versus 1 in 200 short-term chance of dying from the inoculation - Complicating issues: the generally small average life expectancy in Paris Faculty of Medicine and Theology, U. of Paris strongly against Daniel Bernoulli applied his probability model and analysis social_and_medical_statistics_Bernoulli.ppt - calculated the number of persons likely to be killed by smallpox in a given time. - calculated the gain in life expectancy from inoculation for any given age - favoured inoculation Jean D'Alembert disagreed with the analysis Source: 1. http://records.viu.ca/~johnstoi/darwin/sect4.htm 2. www.stats.uwo.ca/faculty/bellhouse/term2008/social_and_medical_statistics. ppt

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Chapter 4 Pairs of Random Variables

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Recall the Definition of a R.V. 10 - 9

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What about these two experiments? Example 2: X Y H T 10 - 10

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(Relate to what you learned in Chapter 1: P(A) = P(A|Bi)P(Bi) = P(A, Bi), where Bi are mutually exlusive and exhaustive)

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10 - 17 Example: If a men and his fiancée are scheduled to meet between 11:30 and 12:00. Suppose that they arrive at random times. What is the probability that they meet within 10 minutes of arrival?

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10 - 18 Q: What would you do to develop the theory for a pair of C.R.Vs

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