Youngkwon C. answered • 12/23/15

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Hi Katie,

As the state 1 and 2 are to attend the class and to be absent, respectively,

a transition matrix, T, for this Markov process has its elements as follows:

t

_{11}= p, t

_{21}= 5p

t

_{12}= 2q, t

_{22}= q

As t

_{11}+ t

_{21}= 1 and t

_{12}+ t

_{22}= 1,

t

_{11}= 1/6, t

_{21}= 5/6

t

_{12}= 2/3, t

_{22}= 1/3

(1) T = ⌈ t

_{11}t

_{12}⌉ = ⌈ 1/6 2/3 ⌉

⌊ t

_{21}t

_{22}⌋ ⌊ 5/6 1/3 ⌋

(2) P(3) = T

^{3}

= T·T·T

= ⌈ 3/8 1/2 ⌉

⌊ 5/8 1/2 ⌋

(3) The answer is the 1st row, 2nd column element of P(3),

which is 1/2.

Hope these help.