Suppose that in a certain part of the country 90% of the children of college edu

Question

Suppose that in a certain part of the country 90% of the children of college educated parents get a college education, but 10% do not. Also, among parents who are not college educated, 40% of their children get college education, but other 60% do not. Assume that the current distribution of parents in that region is 35% who are college educated and 65% who are not. (a) Create a transition diagram for this process. (b) Write down a discrete dynamical system consisting of two difference equations corresponding to the transition diagram. (Use c_n for the fraction of parents who are college-educated and n_n for the fraction of parents that are not college-educated.) (c) What will the distribution of college and non-college educated people be, three generations from now? (d) Suppose that 80% of the children of college educated parents get a college education and among parents who are not college educated, 50% of their children get college education, what will be the distribution of college and non-college educated people be four generations from now?

Explanation / Answer

Ans:Transition Probability Matrix P:

intial distribution=[0.35 0.65]

c)Probability distribution after 3 generations=

a3=a0*P3

P3=

a3=[0.74 0.26]

d)P=

a4=a0*P4

P4=

a4=[0.71 0.29]

educated Not educated educated 0.9 0.1 Not educated 0.4 0.6

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