Take the tour ×  Why do mathematicians say a random variable
takes on a value? Is it just for convenience? My understanding
is that a random variable is a function mapping the sample space
of an experiment to a codomain of interest. When I read "$X$
takes on the value ... ", I take it to mean we apply $X$ to the
outcome $s$ of some experiment, and use the value of this for
some purpose (e.g. assign a probability to it). That is, we use
$a$ when $a=X(s)$.  I don't understand when people say formally
or informally things like $X=4$ or even $X=X(s)$. Isn't this
wrong?  share|improve this question What's the rest of that
sentence? ("$X$ takes on the value...") –  Qiaochu Yuan Sep 16
'12 at 22:25 Functions take on (have) values. For example, let
$f(x)=x^2$. The sentence "Where does $f$ take on the value $9$?"
is quite idiomatic –  André Nicolas Sep 16 '12 at 22:30 Right
André, but doesn't that mean: for what value of $x$ is $f(x)=9$?
In probability I see statements where a closer analogy would be
something like $f