Abstract
In this paper, we will consider a randomized Pólya urn model. Suppose there is a urn with a white balls and b black balls in it initially. Given a special randomized add-ball matrix sequence {An,n≥1} {(X(1,n),X(2,n)),n≥1} and {(Y(1,n),Y(2,n)),n≥1} are randomized vector sequences which satisfied X(1,n)+X(2,n)=Y(1,n)+Y(2,n)=M, for some fixed positive integers M,c, and n=1,2,… We randomly take a ball out from the urn, recording its color, and put it back into the urn at n-th experiment. If the white ball is drawn, then cX(1,n) white balls and cX(2,n) black balls were added into the urn. If the black ball is drawn, then cY(1,n) white balls and cY(2,n) black balls were added into the urn. Repeating this process, and we will study the distribution of white balls in the urn. We will also embed this model into a multitype continuous-time Markov branch process to study. Finally we will apply this model for medical trials.