Question: 3.7.3 Let Xn be an absorbing Markov chain whose transition probability matrix takes the form given in equation (3.76). Let W be the fundamental matrix,

3.7.3 Let Xn be an absorbing Markov chain whose transition probability matrix takes the form given in equation (3.76). Let W be the fundamental matrix, the matrix inverse of I????Q. Let

be the random time of absorption (recall that states r; rC1; : : : ;N are the absorbing states). Establish the joint distribution

whence

image text in transcribed

T= min{n 0; r n N}

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