show all work) In a certain town, it haeen observed that · if a day is sunny, then 4 out of 5 times it is followed by a sunny day, · if a day is cloudy, then it has 70% chance of being followed by another cloudy one. a. Let S® and C) represent the probability of the ith day being sunny or cloudy, respectively. Find the 2 × 2 matrix A such that [S(i+1)] = A b. Show that A is a regular matrix. c. Show that Ais a stochastic matrix. d. Starting with a sunny day, calculate the probability vectors i = 1,2,3. Repeat this calculation starting with a cloudy day instead. e. Find the stable vector of A and compare it to the vectors obtained in for part (d).

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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In a certain town, it haeen observed that
· if a day is sunny, then 4 out of 5 times it is followed by a sunny day,
· if a day is cloudy, then it has 70% chance of being followed by another
cloudy one.
a. Let St) and c® represent the probability of the ith day being sunny
or cloudy, respectively. Find the 2 x 2 matrix A such that
[S(i+1)]
= A
;(i+1
b. Show that A is a regular matrix.
c. Show that Ais a stochastic matrix.
d. Starting with a sunny day, calculate the probability vectors
for
i = 1,2,3. Repeat this calculation starting with a cloudy day instead.
e. Find the stable vector of A and compare it to the vectors obtained in
part (d).
Transcribed Image Text:show all work) In a certain town, it haeen observed that · if a day is sunny, then 4 out of 5 times it is followed by a sunny day, · if a day is cloudy, then it has 70% chance of being followed by another cloudy one. a. Let St) and c® represent the probability of the ith day being sunny or cloudy, respectively. Find the 2 x 2 matrix A such that [S(i+1)] = A ;(i+1 b. Show that A is a regular matrix. c. Show that Ais a stochastic matrix. d. Starting with a sunny day, calculate the probability vectors for i = 1,2,3. Repeat this calculation starting with a cloudy day instead. e. Find the stable vector of A and compare it to the vectors obtained in part (d).
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