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Math Help - Getting a new distribution for X(bar)

  1. #1
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    Red face Getting a new distribution for X(bar)

    Let X(bar) be the mean of a random sample of size 12 from the uniform distribution on the interval (0,1).
    Approximate P(1/2 < X(bar) < 2/3).

    No idea how to do this whatsoever.
    I know you can use the moment generating function but I can't simplify it to make it work.
    And sorry I can't overscore? on here, so X(bar) is sample mean.

    Also, a general idea of how to approach these problems would be helpful too, I have other similar practice problems.

    Any help would be greatly appreciated.
    Thanks in advance!!
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  2. #2
    MHF Contributor matheagle's Avatar
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    The sum of uniforms is not a uniform so I had expected a central limit problem here.
    But with n=12 that's not really appropriate.
    you can multiply by 12 and then figure out

    P\left(6<\sum_{i=1}^{12} X_i<8\right)

    which is a 12 fold integral with density 1.
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  3. #3
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    Quote Originally Posted by matheagle View Post
    The sum of uniforms is not a uniform so I had expected a central limit problem here.
    But with n=12 that's not really appropriate.
    you can multiply by 12 and then figure out

    P\left(6<\sum_{i=1}^{12} X_i<8\right)

    which is a 12 fold integral with density 1.
    That makes sense, thanks for the help!
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  4. #4
    MHF Contributor matheagle's Avatar
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    BUt it still is a pain in the..........
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