CSE 221: Probabilistic Analysis of Computer SystemsIntroductionMemoryless propertypmf and conditional pmfTransition probabilitiesProperties of transition probability matrixGraphical representationExamplesExamples (contd..)CSE 221: Probabilistic Analysis of Computer SystemsTopics covered:Discrete time Markov chains(Sec. 7.1)Introduction Example: State of a component, at every clock tick. Family of random variables: Classification of the process:Memoryless propertyDefinition of memoryless property:Mathematical representation of memoryless property:pmf and conditional pmf pmf of random variable Xn: Conditional transition probability: Homogenous chains:Transition probabilities One-step transition probabilities:Representation as a matrix:Properties of transition probability matrix Stochastic matrix:Graphical representationExamplesCount the number of cars in a service station, at the point of departure of each car.Examples
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