Transcription of Expected Value and Markov Chains - aquatutoring.org
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Expected Value and Markov Chains - aquatutoring.org
Expected Value and Markov ChainsKaren GeSeptember 16, 2016 AbstractAMarkov Chainis a random process that moves from one state toanother such that the next state of the process depends only on wherethe process is at the present state. Anabsorbing stateis a statethat is impossible to leave once reached. We survey common methodsused to find the Expected number of steps needed for a random walkerto reach an absorbing state in a Markov chain . These methods are:solving a system of linear equations, using a transition matrix, andusing a characteristic :probability, Expected Value , absorbing Markov Chains ,transition matrix, state diagram1 Expected ValueIn this section, we give a brief review of some basic definitions, properties,and examples of Expected the random variableXtake on valuesx1,x2,x3,..with probabilitiesp1=P(X=x1),p2=P(X=x2),p3=P( X=x3).
1 1! + 1 2! + 1 3! + = e: 2 Markov Chains A Markov Chain is a random process that moves from one state to another such that the next state of the process depends only on where the process is at present. Each transition is called a step. In a Markov chain, the next step of the process depends only on the present state and it does not matter how
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