Question

Married couple in certain society have no children, one child or 2 children with equal probabilities. Each child is equally likely to be a boy or a girl. Find PGF of Phi(s) ,Graph PGF together with the function g(s) = s. Find the expected size and standard deviation of the male population in the 7-th generation What is the probability that the male line of descent of a particular husband will die out eventually.

Answer 1

In the scenario provided, the probability of having three children is not applicable, and the expected number of children (expected value) for a married couple is 1.

Step-by-step explanation:

The probability that a married adult has three children, as described in the initial conditions of the question, is not applicable since the situation only allows for 0, 1, or 2 children with equal probabilities. Therefore, the expected value in this example represents the mean number of children that married couples are expected to have. To find the expected value, we use the fact that each of these outcomes (0, 1, or 2 children) has equal probability (1/3), so the expected value E(X) would be (0*1/3)+(1*1/3)+(2*1/3) = 1.