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In this paper, we first form a method to calculate the probability generatingfunction of the total progeny of multitype branching process. As examples, wecalculate probability generating function of the total progeny of the multitypebranching processes within random walk which could stay at its position and(2-1) random walk. Consequently, we could give the probability generatingfunctions and the distributions of the hitting time of corresponding randomwalks.

On total progeny of multitype Galton-Watson process and the first passage time of random walk with bounded jumps