To do that, start with∞n=0xn=11-x.Differentiating,∞n=1nxn-1=1(1-x)2.Lettingx= 1-p, we obtainEX=1(1-(1-p))2p=1p.This is reasonable: the number of tosses to get a head should be about1/p.For a “real-life” example, in China, parents are allowed to have only onechild.However, in rural areas, if the child is a girl, they are allowed tohave a second child. Suppose the rule were that parents could have childrenuntil they had a boy. How many girls would a family have on average? Thenumber of children per family has a geometric distribution with
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