Chapter 8.1, Problem 33E

(a)

To determine

To calculate: The distribution after one generation if the initial distribution of birth weights is given by the matrix $\left[\begin{array}{c}0.4\\ 0.4\\ 0.2\end{array}\right]$. Birth Weights can be classified as Low (less than 6 pounds), Average (between 6 and 8 pounds), and High (greater than 8 pounds). Birth weights of female babies tend to be influenced by the birth weights of their mothers.

This tendency is given by the following matrix:

$\begin{array}{l}\text{ Mother}\\ \begin{array}{ccc}H& A& L\end{array}\\ \text{Daughter}\begin{array}{c}H\\ A\\ L\end{array}\left[\begin{array}{ccc}0.5& 0.25& 0.2\\ 0.4& 0.5& 0.2\\ 0.1& 0.25& 0.6\end{array}\right]\end{array}$

(b)

To determine

To calculate: The probability that a woman of High birth weight will have a granddaughter of High birth weight and average birth weight.