Definition talk:Uniform Distribution/Continuous

Question about definition

Surely the statement about $\Img X$ is redundant?

The distribution is defined for all $x \in \R$ -- just that when outside $\closedint a b$ its value is zero.

All we really need to do is state that $a \ne b$ -- although in order to make it slightly more rigorous we really ought to state $a < b$, because if $b < a$ it's not technically a distribution because its integral over $\R$ is not $1$.

So would it be better to amend that second line to:

"Let $a, b \in \R$ such that $a < b$."

? --prime mover (talk) 10:20, 26 June 2019 (EDT)

Oh yeah you're right. For the other pages I didn't define the PDF piecewise like that and handled it by saying $\Img X = \ldots$, because I thought it was neater that way, so added in the image bit out of habit when I came across this page. Note sure why I wrote $a \ne b$ not $a < b$ either. Changed as suggested. Caliburn (talk) 11:35, 26 June 2019 (EDT)