User:Aravind V R/Formulas/Probability

Discrete-time Markov chain
A discrete-time Markov chain is a sequence of random variables X1, X2, X3, ... with the Markov property, namely that the probability of moving to the next state depends only on the present state and not on the previous states
 * $$\Pr(X_{n+1}=x\mid X_1=x_1, X_2=x_2, \ldots, X_n=x_n) = \Pr(X_{n+1}=x\mid X_n=x_n)$$, if both conditional probabilities are well defined, i.e., if $$\Pr(X_1=x_1,\ldots,X_n=x_n)>0$$.