7-5 - 7-5 Random Variables, Probability Distributions,...

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Unformatted text preview: 7-5 Random Variables, Probability Distributions, Expected ValueRANDOMVARIABLESExperiment: flip a coin twiceSample space: {HH, HT, TH, TT}Game: if we get HH or TT, I pay you $1if we get TH, you pay me $2if we get HT, I pay you $.50assign a numerical value X to each outcome:outcomeX (my earnings)HH-1HT-.50TH2TT-1X is called a random variable(r.v. for short)A random variableis an assignment of a real number to each outcome of a sample space7-5p. 1•if we define a r.v. X on a sample space•it makes sense to talk about •the probabilityof various valuesof the r. v. X, •as opposed to the probability of outcomes:P(X = -1) = ½ P(X = -.5) = ¼P(X = 2) = ¼ •can describe the probabilities using functional notation•call our function p:p(-1) = ½ p(-.5) = ¼ p(2) = ¼ pis called the probability functionor probability distributionof random variable X•it is often useful to graphthe probability distribution •here we show the graph in histogramform:7-5p. 21.5x-1-.52.0p(x)EXPECTED...
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This note was uploaded on 12/11/2011 for the course MATH 1324 taught by Professor Staff during the Spring '11 term at Austin Community College.

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7-5 - 7-5 Random Variables, Probability Distributions,...

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