Markov Chains

Part 1:  Television Viewers

Enter the matrix A and the vector p0.

\(A\  = \ {\ {0.85, \ 0.05}, \ {0.15, \ 0.95}\ }; 
\ \ \ \ \ \ \ \ \ \ 
    A\  // \ MatrixForm\)\(p0\  = \ {0.4, \ 0.6}; 
\ \ \ \ \ \ \ \ \ \ p0\  // \ MatrixForm\)

Part 2:  Rental Cars

Enter the matrix M and the vector p0.

\(M\  = 
      \ {\ {0.8, \ 0.3, \ 0.2}, \ 
		\ \ \ \ \ \ \ \ {0.1, \ 0.2, \ 0.6}, 
        \ 
		\ \ \ \ \ \ \ \ {0.1, \ 0.5, \ 0.2}\ }; 
\ \ \ \ \ \ \ \ \ \ 
    M\  // \ MatrixForm\)\(p0\  = \ {0, \ 1, \ 0}; 
\ \ \ \ \ \ \ \ \ \ p0\  // \ MatrixForm\)

Part 3:  Positive Markov Matrices

\(A\  = \ {\ {0, \ 1}, \ {1, \ 0}\ }; \ \ 
\ \ \ \ \ \ \ \ \ \ 
    A\  // \ MatrixForm\)\(p0\  = \ {0.4, \ 0.6}; 
\ \ \ \ \ \ \ \ \ \ p0\  // \ MatrixForm\)

Part 4:  Summary