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Math Help - Conditional distribution of a uniformly distributed random variable

  1. #1
    Senior Member I-Think's Avatar
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    Conditional distribution of a uniformly distributed random variable

    Let U denote a random variable uniformly distributed over (0,1). Compute the conditional distribution of U given that
    U>a
    where 0<a<1

    So if I understand this correctly, we desire

    f_{U|U>a}(U|U>a)=\frac{f(U, U>a)}{f_{U>a}(U>a)}

    How do I proceed from here, assuming I'm correct?
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    Moo
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    Re: Conditional distribution of a uniformly distributed random variable

    Hello,

    You're applying the formula for the conditional density in a bizarre way. It's the conditional density of a random variable with respect to another random variable, not with respect to an event. And here, {U>a} is an event. You can't write that. It makes no sense to take the "density" of U>a !

    U>a should remind you of the cumulative density function. And it's like a density because it determines the distribution of a random variable. And since it works with probabilities, it will be better

    So we're looking for P(U<x|U>a). Of course, the value will depend on whether x>a or not, and if it's in (0,1). But it's not an insurmountable obstacle. And if you want the pdf, you know what to do once you get the conditional cdf
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