Census results reveal that in the United States 80% of the daughters of working women work and that 30% of the daughters of nonworking women work.

a. Write the transition probability for this model.

b. In the long run what fraction of women will be working

A) 0.8 0.2

0.3 0.7

B) 60%

Step-by-step explanation:

Solution Let X0, X1, X2, . . .be random variables representing a “typical" maternal lineage, such that

Xk =(1 if the k-th generation is

working,

(2 if the k-th generation is no

working.

Then{X0, X1, X2, . . .}is a Markov chain with the transition matrix

0.8 0.2

0.3 0.7

It is irreducible and its stationary distribution is π= (0.6,0.4)

By Theorem 8,

limn→∞P(Xn= 1|X0= 1) =limn→∞p1,1(n) = 0.6,

limn→∞P(Xn= 1|X0= 2)=limn→∞p2,1(n) = 0.6.

Thus no matter what the distribution of X0 is,

limn→∞P(Xn= 1) = 0.6

and then in the long run, 60% of women will be working

x+14

step-by-step explanation:

correct answers below: