| Summary: | 碩士 === 中原大學 === 應用數學研究所 === 103 === This paper is aimed Probability (Karr, 1993) from the Chapter 0 of Random Work doing advanced discussions. In addition to Chapter 0 half after the translation into Chinese, after Chapter 0 half we also found an error and some theoremes which were not proved. We gave a complete proof. The errors of Probability (Karr, 1993) occurred in the calculation of the number of back to square one, and it can not be given general formula. We used an example to illustrate this general type is wrong. The second law of reflection in the book mentioned that the result is to obtain P({T^k<∞})=1. The book did not explain how come, so we used Lagrange Inversion Formula (see G. Pólya and G. Szegö, 1972 ) and Cauchy Integral Formula to give rigorous proof. To sum up, we make this section more clearly and understand.
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