1. Lecture 8 Continuous Random Variables Last Time Continuous Random Variables (CRVs) CDF Probability Density Functions (PDF) Expected Values Families of CRVs Reading Assignment: Sections 3.1-3.4 Probability & Stochastic Processes Yates & Goodman (2nd Edition) NTUEE SCC_04_2008 8 - 1

2. Lecture 8: Continuous Random Variables Today Families of CRVs (Cont.) Gaussian R.Vs Delta Function, Mixed Random Variables Probability Models of Derived R.Vs Tomorrow Conditioning a C. R.V. Reading Assignment: Sections 3.5-3.8 Probability & Stochastic Processes Yates & Goodman (2nd Edition) NTUEE SCC_04_2008 8 - 2

3. Lecture 8: Continuous R.V. Next Week 4/17 midterm exam Joint C. D. F. Reading Assignment: 1.1 - 4.1 Probability & Stochastic Processes Yates & Goodman (2nd Edition) NTUEE SCC_04_2008 8 - 3

4. What have you learned about C.R.V.? 8 - 4 Example: An electric power generator may be ON with probability 0.6 OFF with probability 0.4 When it is ON, the power it generates is equally likely to be in [10kW, 20kW] Q1: Let P be the power that is being generated. Derive CDF and PDF of P.

5. What have you learned about C.R.V.? 8 - 5 Example(Cont.) There is no generation cost when the generator is OFF. When it is ON, the cost rate ($/sec) is Q2: Derive the expected cost rate of this generator.

6. What have you learned about C.R.V.? 8 - 6 Lecture 8_supplement.doc

7. Random Number Generation 8 - 7 One of the most common PRNG is the linear congruential generatorlinear congruential generator http://en.wikipedia.org/wiki/Random_number_gen erator RANDOM.ORG - True Random Number Service www.random.org NIST: Random Number Generation and Testing http://csrc.nist.gov/groups/ST/toolkit/rng/index.ht ml

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