‎Given the importance of Markov chains in information theory‎, ‎the definition of conditional probability for these random processes can also be defined in terms of mutual information‎. ‎In this paper‎, ‎the relationship between the concept of sufficiency and Markov chains from the perspective of information theory and the relationship between probabilistic sufficiency and algorithmic sufficiency is determined‎. 

‎In this paper‎, ‎after introducing exponential family and a history of work done by researchers in the field of statistics‎, ‎some applications of this family in statistical inference especially in estimation problem‎,‎statistical hypothesis testing and statistical information theory concepts will be discussed‎.