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Math Help - Uniform distribution

  1. #1
    mtb
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    Uniform distribution

    I just wanted a bit of guidance on the following question.
    I will not ask any more questions after this.

    Suppose X is a normally distributed random variable, mean M and variance s^2.
    Let I(.) denote the distribution function of the standard normal distribution.
    Show that U=I((X-M)/s) has a uniform distribution and give the parameters of the distribution.

    Thanks
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by mtb View Post
    I just wanted a bit of guidance on the following question.
    I will not ask any more questions after this.

    Suppose X is a normally distributed random variable, mean M and variance s^2.
    Let I(.) denote the distribution function of the standard normal distribution.
    Show that U=I((X-M)/s) has a uniform distribution and give the parameters of the distribution.

    Thanks
    First put Z=(X-M)/s

    and suppose a, b \in [0,1],\ b>a

    p(u \in (a,b))=p(z=I^{-1}(u) \in (I^{-1}(a), I^{-1}(b)))

    ................. =b-a

    RonL
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