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Families in a certain society choose the number of children that they will have according to the following rule: If the first child is a girl, they have exactly one more child. If the first child is a boy, they continue to have children until the first girl and then cease childbearing. Let be the number of male children in a particular family. What is the generating function of
?. Determine the mean of
directly and by differentiating the generating function.
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