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A solar heating device can recharge (store heat) in a single sunny day enough to provide for the next two days. In other words, the only times that the solar heat must be augmented by some other heat source is when there are three or more consecutive cloudy days. During the heating season, a period of 120 days, the weather patterns are described by the following Markov chain:
Sunny Cloudy
Suuny 1/2 1/2
Cloudy 1/3 1/3
Using this information, construct another Markov chain which is capable of indicating when the solar heat must be augmented. Hint: Think carefully about your state definition.

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ajeigbeibraheem

Answer:

Step-by-step explanation:

Suppose the number of days is represented with the states(S) provided that a sunny day, with a maximum of three.

i.e.

S = (0, 1, 2, 3)

It implies that; if we assume that [tex]X_n=2[/tex], what this means is that today appears cloudy, then yesterday was cloudly as well while the day before yesterday was sunny.

Constructing a one-step probability transition matrix;

[tex]P = \left\begin{array}{cccc}0\\1\\2\\ 3 \end{array}\right \left[\begin{array}{cccc}1/2&1/2&0 &0\\1/3&0&2/3&0\\1/3&0&0&2/3\\ 1/3 &0&0&2/3\\\end{array}\right][/tex]

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