ee230_slides_chapter3.pdf - Continuous Random Variables and PDFs Cumulative Distribution Functions Normal Random Variables Multiple Continuous Random

ee230_slides_chapter3.pdf - Continuous Random Variables and...

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Continuous Random Variables and PDFs Cumulative Distribution Functions Normal Random Variables Multiple Continuous Random Variables Conditioning The Continuous Bayes’ Rule . . EE 230 General Random Variables Department of Electrical and Electronics Engineering Middle East Technical University April 21, 2016 1/75
Continuous Random Variables and PDFs Cumulative Distribution Functions Normal Random Variables Multiple Continuous Random Variables Conditioning The Continuous Bayes’ Rule . General Random Variables Random variables with a continuous range of possible values are quite common, e.g., thermal noise current intrinsic to all resistors (due to heating of a resistor), your exact weight, .... In fact, some discrete random variables are obtained through some operation on continuous ranges. The use of continuous models may result in insights that would not be possible with discrete modeling. All of the concepts and tools introduced for discrete random variables have continuous counterparts. 2/75
Continuous Random Variables and PDFs Cumulative Distribution Functions Normal Random Variables Multiple Continuous Random Variables Conditioning The Continuous Bayes’ Rule Properties of PDF Some Continuous Random Variables and Their PDFs Expectation . Continuous Random Variables and PDFs . Example . . Angle of an arbitrarily drawn line. Consider that all outcomes are equally likely. What is the probability that the angle will be less than π ? 3/75
Continuous Random Variables and PDFs Cumulative Distribution Functions Normal Random Variables Multiple Continuous Random Variables Conditioning The Continuous Bayes’ Rule Properties of PDF Some Continuous Random Variables and Their PDFs Expectation . Continuous Random Variables and PDFs . Definition . . A random variable X is continuous if there is a nonnegative func. f X , called the probability density function (PDF) of X , such that P ( X B ) = B f X ( x ) dx , for every subset B of the real line. In particular, P ( a X b ) = b a f X ( x ) dx 4/75
Continuous Random Variables and PDFs Cumulative Distribution Functions Normal Random Variables Multiple Continuous Random Variables Conditioning The Continuous Bayes’ Rule Properties of PDF Some Continuous Random Variables and Their PDFs Expectation . Continuous Random Variables and PDFs . Definition . . A random variable X is continuous if there is a nonnegative func. f X , called the probability density function (PDF) of X , such that P ( X B ) = B f X ( x ) dx , for every subset B of the real line. In particular, P ( a X b ) = b a f X ( x ) dx (area under the PDF) 4/75
Continuous Random Variables and PDFs Cumulative Distribution Functions Normal Random Variables Multiple Continuous Random Variables Conditioning The Continuous Bayes’ Rule Properties of PDF Some Continuous Random Variables and Their PDFs Expectation .

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