A cell phone provider classifies its customers as Low users (less than 400 minutesper month) or High users (400 or more minutes per month). Studies have shownthat 80% of the people who were Low users one month will be Low users the nextmonth, and that 70% of the people who were High users one month will be Highusers the next month.
(a) Set up the 2x2 stochastic matrix with columns and rows labeled L and H that displays these transitions
(b) Suppose that, during the month of January, 50% of the customers were Low users. What percent of the customers will be Low users in February? In March? (Type an integer or decimal for each matrix element.)

if the user is low today xt (0) we have the probability of 80% ( 0,8) of have the user in the same condition and 20% (0,2) of having him or her as high user

xt = 1

If the user is high today xt (1) is high today we have the probability of 70% ( 0,7) of having the user in the same condition and 30% (0,3) of having him or her as high user

a) Then we construct the stochastic matrix

Type of user

(xt) xt xt+1

Low (0) or L 0,8 0,2

High(1) or H 0,3 0,7

The resulting equation system is:

xt = 0,8* xt + 0,2* xt+1

xt+1 = 0,3*xt + 0,7* xt+1

1 = xt + xt+1

Solving for variables xt+1 = 1 - xt

xt = 0,8*xt + ( 1 - xt ) * 0,2

xt - 0,8*xt = 0,2 - 0,2xt

xt - 0,6*xt = 0,2

0,4*xt = 0,2

xt = 0,5 and xt+1 = 0,5

b) If in January 0,5 ( 50%) of customesr were low user

In february teh % of low user customer wll be

xt = 0,8* xt + 0,2* xt+1

0,5 = 0,8*0,5 + 0,2*xt+1

0,5 = 0,4 + 0,2 *xt+1

0,1/0,2 = xt+1 xt+1 = 0,5 or 50%

The same answer for March