In a given town there are two newspapers A and B A customer

In a given town there are two newspapers, A and B. A customer who last year subscribed to A, subscribes to A next year with a probability 0.8 and to B with a probability 0-2. Wlien a customer who last year subscribed to B. subscribes next year to A with a probability 0.5 and to B with a probability 0.5. Construct a transition matrix M from year to year and compute the eigenvalues ami eigenvectors of M. Compute m^10. If the original distribution of customers between the two newspapers was 50-50. describe the change of that distribution as time goes by. Is there a steady state?

Solution

(a) given that probability of customers who subscribed to news paper A last year=0.5

same asa A,customers who subscribed to news paper B last year=0.5

customers who will subscribed to news paper A next year=0.8

customers who will subscribed to news paper B next year=0.2

here total probability=10

combining the years of A=0.8+0.5=0.13

B=0.2+0.5=0.7

eigen values are (0.7,0.13,0.2,0.8)

(b)here M^10 is (.(0.7,0.13,0.0.2 0.8)^10

(c)the two papers A ,B does not match each other