Answer:
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
