The flow of a certain river can be one of the following three states: 0: low flow 1: average flow 2: high flow We suppose that the stochastic process {X n , n = 0, 1, . . .}, where Xn represents the...

The flow of a certain river can be one of the following three states:

0: low flow

1: average flow

2: high flow

We suppose that the stochastic process {Xn,
n =
0, 1, . . .}, where
Xn
represents the state of the river flow on the nth day, is a Markov chain. Furthermore, we estimate that the probability that the flow moves from state
i
to state
j
in one day is given by the formula

(a) Calculate the probability that the river flow moves from state 0 to state 1 in one day.

(b) What is the probability that the river flow moves from state 0 to state 2 in two days?