please answer the question and show all work for exercise 9.2.3. iT me andom l e

Question

please answer the question and show all work for exercise 9.2.3.

iT me andom l ell 8t the n day. Write down and explain the ure l he ansition probability matrix. gercise 9.2.3 The transition probability matrix of a discrete-time Markov chain is given by more random e by Y, and ed. and are alternating terest with e process ciating a 0000 1.o 0 0 10 00 P=10001.00 0 0.8 0.2 0 0 0.4 0 0.6 0 0 Draw all sample paths of length 4 that begin in state 1. What is the probability of being in each of the states 1 through 5 after four steps beginning in state 1? rete-time Markoy chain As soon g state Exercise 9.2.4 Consider a disc

Explanation / Answer

All the possible paths along with their probability of occurence here could be obtained as:

These are the only 4 possibilities here.

Now after the 4 unit length paths starting from state 1 , the probability of being in different states would be computed here as:

State 1: 0.16,
State 2: 0.48,
State 3: 0.36
State 4: 0,
State 5: 0

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