Waiting Time Distribution And A Variety Of Probability Generating Function

Nowadays, a lot of attention has been paid to the distribution of some particular patterns in the Random structure. These problems are mostly complex and it is impossible to seek the answer with a classical method. This article recommends the conditional probability generating function method that has been developed in the past decade. By using this method, we deduced the probability generating function of the binomial distribution in the Markov dependent sequence. Subsequently we deduced the early distribution problem in statistics that has attracted much public attention. These statistics include run, pattern and scan. Due to their systematic reliability, the DNA sequence analysis, and the practical value of the radar exploration, the distribution in statistics becomes the current focus. Furthermore, we have listed the calculating software program in algebra. The great effect can be seen in this article caused by the combination of the conditional probability generating function method and the relevant calculation software in algebra.