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Math Help - Can any one help me?

  1. #1
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    Can any one help me?

    hi guys.Can any one help me with this Q?

    To control the population size and make a somewhat traditional population
    happy at the same time, a government passes a law that requires couples to stop having
    children once they have a son. Assuming that sons and daughters are equally likely,
    the distribution of family size is geometric, with pdf given by
    P(M = m) =1/2^m (Geometric distribution)

    Interestingly, the average size of the family is 2, so the population size should stabilise. Since the standard deviation is radical 2, most families should have 5 or less children.

    So how it got 5 children?
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  2. #2
    Master Of Puppets
    pickslides's Avatar
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    Your working thus far is really good.

    Now consider the CDF \displaystyle  F(m)= 1-\left(1-\frac{1}{2}\right)^{m}

    Choose values \displaystyle  m=1,2,3,\dots

    You should find \displaystyle F(5)=0.97 which is 'most' families.
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