Lecture 8 Continuous Random Variables Last Time Continuous Random Variables (CRVs) CDF Probability Density Functions (PDF) Expected Values Families of.

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Presentation transcript:

Lecture 8 Continuous Random Variables Last Time Continuous Random Variables (CRVs) CDF Probability Density Functions (PDF) Expected Values Families of CRVs Reading Assignment: Sections Probability & Stochastic Processes Yates & Goodman (2nd Edition) NTUEE SCC_04_

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 Probability & Stochastic Processes Yates & Goodman (2nd Edition) NTUEE SCC_04_

Lecture 8: Continuous R.V. Next Week 4/17 midterm exam Joint C. D. F. Reading Assignment: Probability & Stochastic Processes Yates & Goodman (2nd Edition) NTUEE SCC_04_

What have you learned about C.R.V.? 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.

What have you learned about C.R.V.? 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.

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

Random Number Generation One of the most common PRNG is the linear congruential generatorlinear congruential generator erator RANDOM.ORG - True Random Number Service NIST: Random Number Generation and Testing ml

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