Markov Models

For the following URN problem with No. states =2, No. time steps =3, No. observations = 3, (O1,O2,O3)=(gray,gray,black) and:

pi = .3 .7

B = (.3 .5 .2, .1 .4 .5) for white, gray and black balls, and

A=(.3 .7, .8 .2)

Use hand calculation of Matlab to:

1. Find the most probable sequence of observations

2. Find the most probable sequence of states

EXTRA CREDIT

Start with a model near the right pi, A, B and see if the Baum-Welch algorithm can find the right solution.