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I am having trouble understanding this notion. How is a distribution function of a random variable a random variable, because we already have the distribution function determined. Also, more importantly, if $X$ is a random variable, how would we find $D(X)$ where $D(a)$ is $Pr (X\leq a)$. I am unable to wrap my mind around this.

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    "How is a distribution function of a random variable a random variable" Basically... it isn't. Where did you get that idea?2012-04-12
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    @RahulNarain : I think your assertion that $D(X)= \Pr(X\le X)$ is simply missing the point.2012-04-12

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