Transcription of EE414 - Probability & Stochastic Processes
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EE414 - Probability & Stochastic Processes
Probability & Stochastic ProcessesIntroduction to Probability TheorySample SpacesEvent SpacesProbability MeasureProbability FunctionsRandom VariablesMoments of Random VariablesIntroduction to Stochastic ProcessesDr Conor McArdleEE414 - Probability & Stochastic Processes1/60 Introduction to Probability TheoryProbability theory is concerned with the description and calculation of the properties ofrandom phenomena, as occur in games of chance, computer and telecommunicationssystems, financial markets, electronic and optical circuits and many other such systems are random, in the sense that it is difficult or impossible topredict exactly how the system will behave in the future, Probability theory can providecharacterisation of the type of randomness involved and yield useful measures, such asaverage values of system parameters or the likelihood of certain events occurring in develop a rigorous mathematical theory of Probability , the starting point is thenotion of arandom experimentand anabstract Probability experimentEis an experiment satisfying the following conditions:all possible distinct outcomes are known a priorithe outcome is not known a priori for any particular trial of the experimentthe experiment is repeatable under identical conditionsDr Conor McArdleEE414 - Probability & Stochastic Processes2/60 Introduction to Probability TheoryMany random phenomena can be modelled
Probability & Stochastic Processes Introduction to Probability Theory Sample Spaces Event Spaces Probability Measure Probability Functions Random Variables
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