Li, X: Probability, Random Signals, and Statistics

With this innovative text, the study-and teaching- of probability and random signals becomes simpler, more streamlined, and more effective. Its unique "e;textgraph"e; format makes it both student-friendly and instructor-friendly. Pages with a larger typeface form a concise text for basic topics and make ideal transparencies; pages with smaller type provide more detailed explanations and more advanced material.

INTRODUCTIONRandomness, Random Signals and SystemsProbability and Random ProcessesTypical Engineering ApplicationsWhy Study Probability and Random SignalsKey Features of the BookRules for the PresentationBASIC CONCEPTS IN PROBABILITYBasics of Set TheoryFundamental Concepts in ProbabilityConditional ProbabilityIndependent EventsTotal Probability Theorem and Bayes' RuleCombined Experiments and Bernoulli TrialsTHE RANDOM VARIABLEConcept of Random VariableCumulative Distribution FunctionProbability Density FunctionUniform DistributionGaussian Distribution and Central Limit TheoremSome Other Commonly Used DistributionsExpectation and MomentsFunctions of a Random VariableConditional DistributionsGeneration of Random NumbersDetermination of Distribution from DataCharacteristic FunctionsMULTIPLE RANDOM VARIABLESJoint Distribution FunctionsJoint Density FunctionIndependence of Random VariablesExpectation and MomentsRelation between Two Random VariablesUniform DistributionsJointly Gaussian Random VariablesFunctions of Random VariablesConditional DistributionsINTRODUCTION TO STATISTICSIntroductionSample Mean and Sample VarianceEmpirical DistributionsStatistical InferenceParameter EstimationHypothesis TestingLinear Regression and Curve FittingRANDOM PROCESSESConcept of Random ProcessCharacterization of Random ProcessesClassification of Random ProcessesCorrelation FunctionsProperties of Autocorrelation FunctionsSample Mean and Sample Correlation FunctionsRelationship between Two Random ProcessesProperties of Crosscorrelation FunctionsGaussian Random ProcessesPOWER SPECTRAL DENSITYConcept of Power Spectral DensityProperties of Power Spectral DensityWhite NoisePower Spectrum EstimationCross-Power SpectrumPower Spectrum in Laplace DomainSome Facts about Fourier TransformsLINEAR SYSTEMS WITH RANDOM INPUTSDeterministic Linear SystemsTime-Domain AnalysisFrequency-Domain AnalysisSummary of Input-Output RelationshipsLinear Systems with White Noise InputEquivalent Noise BandwidthOutput of a Linear System as a Gaussian ProcessOPTIMAL LINEAR SYSTEMSIntroductionSignal-to-Noise RatioThe Matched FilterThe Wiener FilterPlus each chapter includes a summary, additional examples, problems, computer exercises, and self-test problems with solutions.