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...

Extracted 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).