We have studied finite Markov Chain elaborately with almost all its properties. One of the main issues of Markov Chain is the estimation procedure of the transition probabilities. In this study we restrict our self in the most popular estimation procedure and that is the Maximum Likelihood Estimation (MLE) procedure. Here in this study we have also considered two efficient and mostly used test procedures for indentifying the properties of Markov Chain and they are order test and the test of homogeneity or stationarity test. And we apply these estimation procedure and the test procedures to...