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Math Help - Uniform random variable

  1. #1
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    Uniform random variable

    Hi I have a question about uniform random variable

    If X is uniformly distributerd over (a,b) what random variable, having a linear relation with X, is uniformly distributed over (0,1)?

    I knew the answer should be very simple, but I don't know how should I proceed. The fact I do know is that the probability density function of the random variable must be
    f(x) = { 1 0<x<1
    0 otherwise }

    But how should I manipulate so that the new random variable would fall into this interval while having a linear relation with X?

    One attempt I had was U=(X-a)/(b-a) so that U is in the right interval, but I think U doesn't even have a linear relation to X. So yeah, I'm completely clueless. ]
    Thanks.
    Last edited by ChaosticMoon; March 10th 2010 at 01:12 AM.
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  2. #2
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    Quote Originally Posted by ChaosticMoon View Post
    One attempt I had was U=(X-a)/(b-a) so that U is in the right interval, but I think U doesn't even have a linear relation to X. So yeah, I'm completely clueless. ]
    Thanks.
    But that's a linear relation to X : \frac{X-a}{b-a}=\frac{1}{b-a}\cdot X-\frac{a}{b-a}
    which is in the form mx+n

    and if you check with the cumulative density function, you'll see that you're not wrong.
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    Quote Originally Posted by ChaosticMoon View Post
    Hi I have a question about uniform random variable

    If X is uniformly distributerd over (a,b) what random variable, having a linear relation with X, is uniformly distributed over (0,1)?

    I knew the answer should be very simple, but I don't know how should I proceed. The fact I do know is that the probability density function of the random variable must be
    f(x) = { 1 0<x<1
    0 otherwise }

    But how should I manipulate so that the new random variable would fall into this interval while having a linear relation with X?

    One attempt I had was U=(X-a)/(b-a) so that U is in the right interval, but I think U doesn't even have a linear relation to X. So yeah, I'm completely clueless. ]
    Thanks.
    Consider:

    U=\frac{X-a}{b-a}

    Why is this what you seek, in particular what does it mean to say something has a linear association with X?

    CB
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