Question

The Markov Chain with states labelled 1, 2, 3 and 4 has the following one-step transition matrix P = egin{pmatrix} 1/4 & 1/4 & 1/4 & 1/4 \ 0 & 1 & 0 & 0 \ 1/4 & 0 & 1/2 & 1/4 \ 0 & 0 & 0 & 1 end{pmatrix} (a) Rewrite P into the canonical form and classify the states. (b) Calculate lim_{n o infty} P^n. (c) Calculate eventual transition probabilities f_{11} and f_{22}. (d) Calculate eventual transition probabilities f_{32} and f_{34}. (e) Calculate E[N_3], the average amount of time the chain spends in state 3. 

          The Markov Chain with states labelled 1, 2, 3 and 4 has the following one-step transition matrix
P = egin{pmatrix} 1/4 & 1/4 & 1/4 & 1/4 \ 0 & 1 & 0 & 0 \ 1/4 & 0 & 1/2 & 1/4 \ 0 & 0 & 0 & 1 end{pmatrix}
(a) Rewrite P into the canonical form and classify the states.
(b) Calculate lim_{n 	o infty} P^n.
(c) Calculate eventual transition probabilities f_{11} and f_{22}.
(d) Calculate eventual transition probabilities f_{32} and f_{34}.
(e) Calculate E[N_3], the average amount of time the chain spends in state 3.
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The Markov Chain with states labelled 1, 2, 3 and 4 has the following one-step transition matrix P = eginpmatrix 1/4 1/4 1/4 1/4 0 1 0 0 1/4 0 1/2 1/4 0 0 0 1 endpmatrix (a) Rewrite P into the canonical form and classify the states. (b) Calculate limn o infty P^n. (c) Calculate eventual transition probabilities f11 and f22. (d) Calculate eventual transition probabilities f32 and f34. (e) Calculate E[N3], the average amount of time the chain spends in state 3.

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Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
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The Markov Chain with states labelled 1, 2, 3 and 4 has the following one-step transition matrix P = (1/4 1/4 1/4 1/4; 0 1 0 0; 1/4 0 1/2 1/4; 0 0 0 1) (a) Rewrite P into the canonical form and classify the states. (b) Calculate lim n->infinity P^n. (c) Calculate eventual transition probabilities f11 and f22. (d) Calculate eventual transition probabilities f32 and f34. (e) Calculate E[N3], the average amount of time the chain spends in state 3.
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Transcript

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0:00 Hello students.
00:02 Today we will discuss about this question.
00:05 In this question we are given a markov chain with states label that is 1, 2, 3 and 4 that has the following one step transition.
00:15 So here p is equals to 1 divide by 4 1 divide by 4 1 divide by 4 1 divide by 4 0 1 0 0 0 0 0 0 0 0 0 1 divide by 4.
00:25 0 1 divide by 4 1 divide by 4 0 1 divide by 4.
00:27 0 1 divide by 4.
00:30 0 .001.
00:33 So here we need to rewrite p into connoanalical form.
00:38 So here we need to rewrite p into canonical form and classify the states.
00:51 That is equal to question mark.
00:54 So here first of all here we can write p that is equal to here one two three four here it is also 1, 2, 3 and 4...
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