L18_VarianceRVs

L18_VarianceRVs - 1-1COMP170Discrete Mathematical Toolsfor...

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Unformatted text preview: 1-1COMP170Discrete Mathematical Toolsfor Computer ScienceDiscrete Math for Computer ScienceK. Bogart, C. Stein and R.L. DrysdaleSection 5.7, pp. 294-303Variance of RVsVersion 2.0: Last updated, May 13, 2007Slidesc2005 by M. J. Golin and G. Trippen2-1Probability Distributions and Variance2-2Probability Distributions and Variance•Distributions of Random Variables2-3Probability Distributions and Variance•Distributions of Random Variables•Variance3-1Distributions of Random Variables3-2Distributions of Random VariablesExpected value3-3Distributions of Random VariablesExpected valueExample:Flip a coin100times, expected number ofHis50.3-4Distributions of Random VariablesExpected valueExample:Flip a coin100times, expected number ofHis50.To what extent do we expect to see50heads?3-5Distributions 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?3-6Distributions 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.4-1Thedistribution functionDof a random variableXwith finitely many values is the function on thevalues ofXdefined byD(x) =P(X=x).4-2Thedistribution 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.4-3Thedistribution 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.4-4Thedistribution 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).5-1Examples:5-2Examples:10coin flips5-3Examples:10coin flips5-4Examples:10coin flipsTen-question test with probability.8of getting a correct answer.5-5Examples:10coin flipsTen-question test with probability.8of getting a correct answer.5-6Examples:10coin flipsTen-question test with probability.8of getting a correct answer....
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L18_VarianceRVs - 1-1COMP170Discrete Mathematical Toolsfor...

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