Definition talk:Probability Density Function

Is this defined only when that complicated limit actually exists? Is it the case that it does always exist? --prime mover (talk) 13:55, 20 December 2012 (UTC)


 * Corrected to point out that it doesn't always exist. The definition is neater when the pdf is considered as the derivative of the cdf, but I was going to add that as a theorem, with a sufficient condition for the pdf existing is that the cdf is differentiable. If you have a more elegant approach by all means please suggest it. The motivation of this definition is to get around the problem that $Pr(X=c) = 0$, should I mention it on the page so that the limit isn't coming out of nowhere? --GFauxPas (talk) 14:37, 20 December 2012 (UTC)


 * Having thought about it, if $X$ is continuous, then it probably does exist througout. No worries, just thought I'd ask. If you're quoting what Bean says, then trust him not me ... --prime mover (talk) 17:37, 20 December 2012 (UTC)


 * It wasn't just what you said; I realize now I was confusing piecewise-continuous and continuous. I'll fix it later --GFauxPas (talk) 17:48, 20 December 2012 (UTC)