Hello, inso!

w = work, .n = not work.Census studies from 1960 reveal that in France 70% of the daughters of working women

also work, and 50% of the daughters of nonworking women work.

Assume that this trend remains unchanged from one generation to the next,

(a) Set up a Markov chain by drawing the transition diagram and the transition matrix.

. .

We have: .

The transition matrix is: .

(b) At that time 40% of French women worked.

Determine the percentage of working women in the next two generations.

We have: . at the first generation.

Second generation: .

. . Working women: 58%

Third generation: .

. . Working women: 61.6%

We want the "steady state" vector.(c) In the long run what percentage of French women will work?

This is a vector such that: .

So we have: .

Then we have: . . These two equatons arealwaysequivalent.

The second equation is: .always

Solve the system: .

Eventually, 62.5% of the women will be working.