Explain and show me all the steps. Prove that the Markov property P(x_(n+1)=j|x_(0)=i_(0),x_(1)=i_(1),dots,x_(n)=i)=P(x_(n+1)=j|x_(n)=i) implies P(x_(n+m)=j|x_(0)=i_(0),x_(1)=i_(1),dots,x_(n)=i)=P(x_("
Which of the following options correctly completes the statement?
A) P(x_(n+m)=j|x_(0)=i_(0),x_(1)=i_(1),dots,x_(n)=i) = P(x_(n+1)=j|x_(n)=i)
B) P(x_(n+m)=j|x_(0)=i_(0),x_(1)=i_(1),dots,x_(n)=i) = P(x_(n+1)=j|x_(0)=i_(0),x_(1)=i_(1),dots,x_(n)=i)
C) P(x_(n+m)=j|x_(0)=i_(0),x_(1)=i_(1),dots,x_(n)=i) = P(x_(n+1)=j|x_(n)=i_(0),x_(1)=i_(1),dots,x_(n)=i)
D) P(x_(n+m)=j|x_(0)=i_(0),x_(1)=i_(1),dots,x_(n)=i) = P(x_(n+1)=j|x_(n)=i_(0),x_(1)=i_(1),dots,x_(n)=i)
