I am trying to get the CDF of a random variable using TransformedDistribution.
Probability[-t v <= y - x <=
t v, {x \[Distributed] UniformDistribution[{0, l}],
y \[Distributed] UniformDistribution[{0, l}]}] //
Simplify[#, l > 0 && t > 0 && v > 0 && t v < l] &
The result is
$$\left\{ \begin{matrix} \frac{t v (2 l-t v)}{l^2} & l\neq 2 t v \\ \frac{2 t^2 v^2}{l^2}+\frac{1}{4} & l=2 t v \\ 0 & \text{True} \\ \end{matrix}\right. $$
Why does Simplify give an answer as a separate case when $l=2tv$? If I plug $l=2 tv$ into the first and second answers, they will come to the same result.
FullSimplify
instead ofSimplify
$\endgroup$Rational[3,4]
, which is the same result if I putl=2tv
into the first expression above. So the problem remains. $\endgroup$FullSimplify
indeed gives two cases which are equivalent atl=2tv
. One requires calculation to resolve, the other doesn't. I'd not want it done another way, particularly when the calc. involved might be time-consuming... $\endgroup$