ON THE LIMIT OF THE MARKOV BINOMIAL-DISTRIBUTION

Let X//1, X//2, . . . be a Markov Benoulli sequence with initial probabilities rho of success and q equals 1 minus rho of failure, and probabilities 1 minus (1 minus pi ) rho , (1 minus pi 0 rho in the first row and (1 minus pi )(1 minus rho ), (1 minus pi ) rho plus pi in the second row of the transition matrix. If S//n equals SIGMA X//i, where the sum is from i equals 1 to n, then the limit distribution P left brace S//n equals k right brace is obtained when n approaches infinity , n rho approaches lambda .