  We present 15 explicit examples of discrete time Birth and Death processes
which are exactly solvable. They are related to the hypergeometric orthogonal
polynomials of Askey scheme having discrete orthogonality measures. Namely,
they are the Krawtchouk, three different kinds of q-Krawtchouk, (dual, q)-Hahn,
(q)-Racah, Al-Salam-Carlitz II, q-Meixner, q-Charlier, dual big q-Jacobi and
dual big q-Laguerre polynomials. The birth and death rates are determined by
the difference equations governing the polynomials. The stationary
distributions are the normalised orthogonality measures of the polynomials. The
transition probabilities are neatly expressed by the normalised polynomials and
the corresponding eigenvalues. This paper is simply the discrete time versions
of the known solutions of the continuous time birth and death processes.
