# Is distribution of CDF uniform [closed]

If I think CDF as a random variable, what is the distribution of CDF ? Is it uniform ?

Let $Y:\Bbb R \to \Bbb R$ and $X: \Bbb R \to \Bbb R$ where the latter is defined by $X(r)=F_Y(r)=P(Y \leq r)$ (so the range of $X$ is $[0,1]$ now). Now if I ask the question about the probability $P(X \leq c)=P(r:X(r)<c)$.

Note that Sample space is $\Bbb R$ here. Does this make sense now ?

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Please try to restate your question. As it is written, I can not make any sense of it. What do you mean by "think [of a] CDF as a random variable", for instance? –  Nicholas R. Peterson Sep 11 at 3:06
I think what Prasenjit means is if the distribution of a (random) cumulative density function is Uniform. Random cdf is $F(X)$ where X is a random variable having cdf F. In this case, $F(X)$ will always have uniform distribution over (0,1). This can be derived very easily by considering the cdf of F(X) and taking inverse approach. One quick intuition is for cdf being a probability, it always lies in (0,1); so is Uniform(0,1). Hope this makes sense. –  Sauvik De Nov 28 at 4:40