Lecture 8

Continuous Random Variables

Last Time

Continuous Random Variables (CRVs) CDF Probability Density Functions (PDF) Expected Values Families of CRVs

Reading Assignment: Sections 3.1-3.4Probability & Stochastic ProcessesYates & Goodman (2nd Edition) NTUEE SCC_04_20088 - 1

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 ProcessesYates & Goodman (2nd Edition) NTUEE SCC_04_20088 - 2

Lecture 8: Continuous R.V.

Next Week 4/17 midterm exam Joint C. D. F.

Reading Assignment: 1.1 - 4.1

Probability & Stochastic ProcessesYates & Goodman (2nd Edition) NTUEE SCC_04_20088 - 3

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

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Example: An electric power generator may be ON with probability 0.6 OFF with probability 0.4When 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.?

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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.?

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Lecture 8_supplement.doc

Random Number Generation

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One of the most common PRNG is the linear congruential generatorhttp://en.wikipedia.org/wiki/Random_number_generator

RANDOM.ORG - True Random Number Servicewww.random.org

NIST: Random Number Generation and Testinghttp://csrc.nist.gov/groups/ST/toolkit/rng/index.html

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