Problem A:
A Markov chain \(X_{0}, X_{1}, X_{2}, \ldots\) with state space \{0,1,2\} has the following transition matrix
$$ \boldsymbol{P}=\begin{array}{cccc} & 0 & 1 & 2 \\ 0 & 0.1 & 0.2 & a \\ 1 & 0.9 & 0.1 & 0 \\ 2 & 0.1 & 0.8 & b \end{array} $$
and initial distribution \(\alpha_{0}=P\left(X_{0}=0\right)=0.3, \alpha_{1}=P\left(X_{0}=1\right)=0.4,\) and \(\alpha_{2}=P\left(X_{0}=2\right)=\)
c. Find the following:
a) values \(a, b\) and \(c\).
b) \(P\left(X_{0}=0, X_{1}=1, X_{2}=2\right)\) and \(P\left(X_{0}=0, X_{1}=2, X_{2}=1\right)\).
c) \(P\left(X_{1}=2\right)\)
d) \(P\left(X_{2}=1, X_{3}=1 \mid X_{1}=2\right)\) and \(P\left(X_{1}=1, X_{2}=1 \mid X_{0}=2\right)\).
Homework Answers
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Problem A A Markov chain Xo,X1,X2,... with state space 0,1,2) has the following transition matrix 0...
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012
0 0.3 0.2 0.5
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0),P(X3 = 2|X1 = 0).
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I need help with these problem. A Markov chain Xo, X1, X2,... has the transition probability...
I need help with these problem.
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A Markov chain X0, X1, X2,... has transition matrix
012
0 0.3 0.2 0.5
P = 1 0.5 0.1 0.4 .2 0.3 0.3 0.4
(i) Determine the conditional probabilities P(X1 = 1,X2 = 0|X0 =
0),P(X3 = 2|X1 = 0).
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1/2. Determine the probabilities P(X0 = 1, X1 = 1, X2 = 2) and P(X3
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I need help with these problem.
A Markov chain Xo, X1, X2,... has the transition probability matrix 0 0.7 0.2 0.1 P 10 0.6 0.4 20.5 0 0.5 Determine the conditional probabilities
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a. Compute.
b. Compute.
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