Our new technology (unified statistics theory by MCMC) generates new knowledge as well as the computational tools to create that knowledge and forms new modern and emerging scientific field of information technology and of AI. Skillfully, the basic of finite Markov chains (all types and properties) for the great development of this book to form a comprehensive picture is presented. Three proposed algorithms are designed and executed in order to introduce a complete framework toward a new philosophy of a surely successful rigorous methods and theory of MCMC, of statistical inference about...