Please answer this statistics and probability question:

7. The socialist Elizabeth Wrigley-Field posed the following puzzle: American fertility fluctuated dramatically in the decades surrounding the Second World War. Parents created the smallest families during the Great Depression, and the largest families during the postwar Baby Boom. Yet children born during the Great Depression came from larger families than those born during the Baby Boom. How can this be? (a) Consider the Great Depression era. Let 71;; be the number of American families with exactly k children for each It 2 0. For each] 2 0, let on "If = Z kink k=0 For afamily selected randomly in that era (with all families equally likely), nd the expected number of children in the family. Express your answer only in terms ofthe mj's. [3 pts] (b) For a child selected randomly in that era, nd the expected number of children in the child's family, only in terms of the mj's. [3 pts] (c) Give an intuitive explanation in words for which of the answers to (a) and (b) is larger, or whether they are equal. Explain how this relates to the Wrigley-Field puzzle. [4 pts]