关于Polya罐子模型的几个结论

在Polya罐子模型中,分别以Xn,Sn表示第n次抽球并放回后罐中的黑球比例数和在前n次抽球中抽到黑球的次数,得到了Sn/n的极限分布为贝塔分布以及E（Xn）等于E（X∞）,D（Xn）不等于D（X∞）等几个重要结论,并分别运用概率论知识和随机过程的鞅理论知识从不同角度证明结论.

Several Results of Polya Urn Mode

In Polya Urn Model, Xn and Sn were used to denote the fraction of black balls and the number of black balls chosen in the first n drawings. The limit distribution of Sn/n had a Beta distribution , E（Xn）was equal to E （X∞）and E（X∞）, D （Xn ） was not equal to D（X∞）. From the different angles, some correlated knowledge of probability theory and martingale theory of stochastic processes were applied for proving these important results respectively.