Question

Data have been accumulated on the heights of children relativeto their parents. Suppose that the probabilities that a tall parentwill have a tall, medium-height, or short child are 0.6, 0.2, and0.2, respectivly; the probabilities that a medium-height parentwill have a tall, medium-height, or short child are 0.1, 0.7, and0.2, respectively; and the probabilities that a short parent willhave a tall, medium-height, or short child are 0.2, 0.4, and 0.4respectively.

a) Write down the transition martix for this Markovchain.

b) What is the probability that a short person will have atall grandchild?

c) If 20% of the current population is tall, 50% is of mediumheight, and 30% is short, what will the distribution be in threegenerations?

d) If the data in part (c) do not change over time, whatproportion of the population will be tall, of medium height, andshort in the long run?

Answer 1