Assumption: If at some time t 0 {\displaystyle t_{0}\ } , the Markov chain is in state E i {\displaystyle E_{i}\ } , then the probability that at time t 0 + t {\displaystyle t_{0}+t\ } , it will be in state E j {\displaystyle E_{j}\ } depends only upon i {\displaystyle i\ } , j {\displaystyle j\ } and t {\displaystyle t\ } . This then allows us to write that probability as p i j ( t ) {\displaystyle p_{ij}(t)\ } .