Question

Test the following transition matrix

Answer 1

Answer:

We often list the transition probabilities in a matrix. The matrix is called the state transition matrix or transition probability matrix and is usually shown by PP. Assuming the states are 11, 22, ⋯⋯, rr, then the state transition matrix is given by

P=⎡⎣⎢⎢⎢⎢⎢⎢⎢⎢p11p21...pr1p12p22...pr2............p1rp2r...prr⎤⎦⎥⎥⎥⎥⎥⎥⎥⎥.P=[p11p12...p1rp21p22...p2r............pr1pr2...prr].

Note that pij≥0pij≥0, and for all ii, we have

∑k=1rpik=∑k=1rP(Xm+1=