Consider the following Markov chain with P{X0 = 2} = 0.6 andP{X0 = 4} = 0.4:
1 2 3 4 5 6
1 0 0 0 0 1 0
2 .2 .05 0 .6 0 .15
3 0 0 .8 0 0 .2
4 0 .6 0 .2 0 .2
5 1 0 0 0 0 0
6 0 0 .7 0 0 .3
a. What is P{X1 = 4, X2 = 6 | X0 = 2}?
b. What is P{X2 = 6 | X0 = 2}? What is P{X18 = 6 | X16 = 2}?
c. What is P{X0 = 2, X1 = 4, X2 = 6}?
d. What is P{X1 = 4, X2 = 6}?
