Question

Data have been accumulated on the heights of children relative to their parents. Suppose that the probabilities that a tall parent will have a tall, medium-height, or short child are 0.5, 0.3, and 0.2, respectively; the probabilities that a medium-height parent will have a tall, medium-height, or short child are 0.1, 0.7, and 0.2, respectively; and the probabilities that a short parent will have a tall, medium-height, or short child are 0.1, 0.4, and 0.5, respectively. (a) Write down the transition matrix for this Markov chain. (Order rows by tall first, medium second, and short third.) $egin{bmatrix} 0.5 & 0.1 & 0.1 \ 0.3 & 0.7 & 0.4 \ 0.2 & 0.2 & 0.5 end{bmatrix}$ (b) What is the probability that a short person will have a tall grandchild? (c) If 30% of the current population is tall, 40% is of medium height, and 30% is short, what will the distribution be in three generations? (d) What proportion of the population will be tall, of medium height, and short in the long run?

          Data have been accumulated on the heights of children relative to their parents. Suppose that the probabilities that a tall parent will have a tall, medium-height, or short child are 0.5,
0.3, and 0.2, respectively; the probabilities that a medium-height parent will have a tall, medium-height, or short child are 0.1, 0.7, and 0.2, respectively; and the probabilities that a
short parent will have a tall, medium-height, or short child are 0.1, 0.4, and 0.5, respectively.
(a) Write down the transition matrix for this Markov chain. (Order rows by tall first, medium second, and short third.)
$egin{bmatrix} 0.5 & 0.1 & 0.1 \ 0.3 & 0.7 & 0.4 \ 0.2 & 0.2 & 0.5 end{bmatrix}$
(b) What is the probability that a short person will have a tall grandchild?
(c) If 30% of the current population is tall, 40% is of medium height, and 30% is short, what will the distribution be in three generations?
(d) What proportion of the population will be tall, of medium height, and short in the long run?

Data have been accumulated on the heights of children relative to their parents. Suppose that the probabilities that a tall parent will have a tall, medium-height, or short child are 0.5,
0.3, and 0.2, respectively; the probabilities that a medium-height parent will have a tall, medium-height, or short child are 0.1, 0.7, and 0.2, respectively; and the probabilities that a
short parent will have a tall, medium-height, or short child are 0.1, 0.4, and 0.5, respectively.
(a) Write down the transition matrix for this Markov chain. (Order rows by tall first, medium second, and short third.)
eginbmatrix 0.5 0.1 0.1 0.3 0.7 0.4 0.2 0.2 0.5 endbmatrix
(b) What is the probability that a short person will have a tall grandchild?
(c) If 30% of the current population is tall, 40% is of medium height, and 30% is short, what will the distribution be in three generations?
(d) What proportion of the population will be tall, of medium height, and short in the long run?

Added by Jasmine H.

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