A Markov chain has generator matrix (a) Exhibit the Kolmogorov backward equations. (b) Find the transition function by diagonalizing the generator and finding the matrix exponential. (c) Find the...

A Markov chain has generator matrix

(a) Exhibit the Kolmogorov backward equations.

(b) Find the transition function by diagonalizing the generator and finding the matrix exponential.

(c) Find the transition function using a symbolic software system such as Wolfram Alpha.