I am confused .. how does this happen?
"continuous cumulative distribution functions (cdfs) range uniformly over the open interval (0,1).".
How does the cdf range "uniformly" (each value having the same probability of occurance) between [0,1]?
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Without more context for the quote it's difficult to be 100% certain what is intended by the comment, but I believe this is a reference to the distribution function $F_X(x)$ applied as a transformation of $X$. That is, $F_X(X)$ is standard uniform. See [here](http://stats.stackexchange.com/questions/77845/inverse-function-for-a-non-decreasing-cdf), but there are many other relevant posts on site, e.g. [here](http://stats.stackexchange.com/questions/83538/distribution-function-applied-to-itself) and ... (ctd) – Glen_b Jun 06 '15 at 04:58
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(ctd) ... [here](http://stats.stackexchange.com/questions/73778/cumulative-distribution-function-inequality-discrete-distributions) and more generally, searching for *probability integral transform* should turn up several additional relevant posts. If you're really asking about something else, you'll need to clarify your post (and offer more context). – Glen_b Jun 06 '15 at 04:58