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Unformatted text preview: 11COMP170Discrete Mathematical Toolsfor Computer ScienceDiscrete Math for Computer ScienceK. Bogart, C. Stein and R.L. DrysdaleSection 5.7, pp. 294303Variance of RVsVersion 2.0: Last updated, May 13, 2007Slidesc2005 by M. J. Golin and G. Trippen21Probability Distributions and Variance22Probability Distributions and Variance•Distributions of Random Variables23Probability Distributions and Variance•Distributions of Random Variables•Variance31Distributions of Random Variables32Distributions of Random VariablesExpected value33Distributions of Random VariablesExpected valueExample:Flip a coin100times, expected number ofHis50.34Distributions of Random VariablesExpected valueExample:Flip a coin100times, expected number ofHis50.To what extent do we expect to see50heads?35Distributions of Random VariablesExpected valueExample:Flip a coin100times, expected number ofHis50.To what extent do we expect to see50heads?Is it surprising to see55,60, or65heads instead?36Distributions of Random VariablesExpected valueExample:Flip a coin100times, expected number ofHis50.To what extent do we expect to see50heads?Is it surprising to see55,60, or65heads instead?General Question: how much do we expect a randomvariable todeviatefrom its expected value.41Thedistribution functionDof a random variableXwith finitely many values is the function on thevalues ofXdefined byD(x) =P(X=x).42Thedistribution functionDof a random variableXwith finitely many values is the function on thevalues ofXdefined byD(x) =P(X=x).The distribution function of the random variableXassigns to each valuexof the random variable theprobability thatXachieves that value.43Thedistribution functionDof a random variableXwith finitely many values is the function on thevalues ofXdefined byD(x) =P(X=x).The distribution function of the random variableXassigns to each valuexof the random variable theprobability thatXachieves that value.Visualize the distribution function using a diagramcalled ahistogram.44Thedistribution functionDof a random variableXwith finitely many values is the function on thevalues ofXdefined byD(x) =P(X=x).The distribution function of the random variableXassigns to each valuexof the random variable theprobability thatXachieves that value.Visualize the distribution function using a diagramcalled ahistogram.Graphs that show, for each integer valuexofX,a rectangle of width1centered atx, whose height(and thus area) is proportional to the probabilityP(X=x).51Examples:52Examples:10coin flips53Examples:10coin flips54Examples:10coin flipsTenquestion test with probability.8of getting a correct answer.55Examples:10coin flipsTenquestion test with probability.8of getting a correct answer.56Examples:10coin flipsTenquestion test with probability.8of getting a correct answer....
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 Spring '10
 M.J.Golin
 Computer Science

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