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Let 0,1, be a sequence of nonnegative numbers such that j=0 ...
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Let ?0?,?1?,? be a sequence of nonnegative numbers such that ?j=0???j?=1. Consider a Markov chain X0?,X1?,X2?,? with the state space S={0,1,2,?} such that pij?=?j?, for all j?S. Show that X1?,X2?,? is a sequence of i.i.d random variables.