Consider the Markov chain (Xn)n≥o with state space S = {0, 1, 2} and transition probability matrix 10 23 P 9 19 1 19 1 Define by T the time the process first reaches the absorbing state 2. Compute the following: = 12 23 9 19 1 23 (a) the expected times until absorption E[T|Xo = 0] = 229/11 E[T| Xo = 1] = 227/11 (b) the probabilities P(T > 2 | X₁ = 0) : P(T > 2 | X₁ = 1) = (c) the probability P(T≥ 3) = = 9148/1 7488/8 given that P(X₁ = 0) = 0.2 and P(X。 = 1) = 0.8.
Consider the Markov chain (Xn)n≥o with state space S = {0, 1, 2} and transition probability matrix 10 23 P 9 19 1 19 1 Define by T the time the process first reaches the absorbing state 2. Compute the following: = 12 23 9 19 1 23 (a) the expected times until absorption E[T|Xo = 0] = 229/11 E[T| Xo = 1] = 227/11 (b) the probabilities P(T > 2 | X₁ = 0) : P(T > 2 | X₁ = 1) = (c) the probability P(T≥ 3) = = 9148/1 7488/8 given that P(X₁ = 0) = 0.2 and P(X。 = 1) = 0.8.
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Please solve for (c)
![Consider the Markov chain (Xn)n≥o with state space S = {0, 1, 2} and transition probability matrix
10 12
23
23
P
9
9
19
19
0
0
Define by T the time the process first reaches the absorbing state 2. Compute the following:
=
1
23
1
19
1
(a) the expected times until absorption
E[T|Xo=0] = 229/11
E[T| Xo = 1] = 227/11
(c) the probability
P(T ≥ 3) =
(b) the probabilities
P(T > 2 | X。 = 0) =
P(T > 2 | Xo = 1) =
9148/1
7488/8
given that P(Xo = 0) = 0.2 and P(Xo = 1) = 0.8.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F91f76606-a4d9-42f0-be0d-7b1366a5593f%2Fecb5db8e-0aa5-4726-a7de-434938c57732%2Fmxwqy8j_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the Markov chain (Xn)n≥o with state space S = {0, 1, 2} and transition probability matrix
10 12
23
23
P
9
9
19
19
0
0
Define by T the time the process first reaches the absorbing state 2. Compute the following:
=
1
23
1
19
1
(a) the expected times until absorption
E[T|Xo=0] = 229/11
E[T| Xo = 1] = 227/11
(c) the probability
P(T ≥ 3) =
(b) the probabilities
P(T > 2 | X。 = 0) =
P(T > 2 | Xo = 1) =
9148/1
7488/8
given that P(Xo = 0) = 0.2 and P(Xo = 1) = 0.8.
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