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8. Consider a population of n couples where a boy is born to the ith couple with probability p; and c, is the expected number of children born to this couple. Assume p, is constant with time for all couples and that sexcs of successive children born to a particular couple are independent r.vs. Further, assumethat no multiple births are allowed. The sex ratio is defined to be expected number of boys born in the population of n couples expected number of children born in the population of n couples Suppose c,-c, i-1, 2, ..., n. Find S.

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Total number of couples is n. The probability that a boy is born to the ih (i = 1, 2, ..., n) couple is p. The expected numbe

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