7.3. Let X, be an absorbing Markov chain whose transition probability matrix takes the form given in equation (7.1). Let W be the fundamental matrix, the matrix inverse of I - Q. Let T=min{n?0;rSn -5 N}

be the random time of absorption (recall that states r, r + 1, ... , N are the absorbing states). Establish the joint distribution Pr{XT_, = j, XT = kIXO = i} = W;Pk for 0 <- i, j < r; r:5 k : N, whence N Pr{XT_, = j1X0 = i} = 7, W,.;Pk for 0:i,jk=r