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elemprob-fall2010-page8

elemprob-fall2010-page8 - To do that start with xn = n=0...

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To do that, start with n =0 x n = 1 1 - x . Differentiating, n =1 nx n - 1 = 1 (1 - x ) 2 . Letting x = 1 - p , we obtain E X = 1 (1 - (1 - p )) 2 p = 1 p . This is reasonable: the number of tosses to get a head should be about 1 /p . For a “real-life” example, in China, parents are allowed to have only one child. However, in rural areas, if the child is a girl, they are allowed to have a second child. Suppose the rule were that parents could have children until they had a boy. How many girls would a family have on average? The number of children per family has a geometric distribution with
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