Youngkwon C. answered • 12/01/15

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Hi Katie,

Let S

Let S

_{i}, i = 1, 2, denote the state i,where i = 1 and i = 2 are for meadows and woods, respectively.

If T

transition probabilities are given as follows.

Prob(T

Prob(T

Prob(T

Prob(T

If T

_{ij}denotes the transition from S_{j}to S_{i},transition probabilities are given as follows.

Prob(T

_{11}) = 2/3Prob(T

_{21}) = 1- Prob(T_{11}) = 1 - 2/3 = 1/3Prob(T

_{12}) = 1/4 = 1- Prob(T_{22}) = 1 - 3/4 = 1/4Prob(T

_{22}) = 3/4(1) So, the Markovian transition matrix, M, is

⌈

**2/3 1/4**⌉ ⌊

**1/3 3/4**⌋(2) M

^{3}= M^{2}·M = ⌈ 19/36 17/48 ⌉ · ⌈ 2/3 1/4 ⌉

⌊ 17/36 31/48 ⌋ ⌊ 1/3 3/4 ⌋

= ⌈ 203/432 229/576 ⌉

⌊ 229/432 347/576 ⌋

M

^{3}_{22}from the matrix M^{3}represents the probability of the given event, which is

**0.6024**(= 347/576).(3) M

^{3}_{12}from the matrix M^{3}represents the probability of the given event, which is

**0.3976**(= 229/576).