# Renaming one parameter changes the result of Simplify

Surely the following couple of expressions should both output True:

Simplify[
PDF[TransformedDistribution[(A + B)/2, {A, B} \[Distributed]
UniformDistribution[{{L, H}, {L, H}}]], t] ==
PDF[TriangularDistribution[{L, H}], t], L < t < H]


and

Simplify[
PDF[TransformedDistribution[(A + B)/2, {A, B} \[Distributed]
UniformDistribution[{{L, U}, {L, U}}]], t] ==
PDF[TriangularDistribution[{L, U}], t], L < t < U]


They aren't. At least not on my version 11.1.1.0. Only the first expression outputs True.

• Note that PDF[TransformedDistribution[(A + B)/2, {A, B}  UniformDistribution[{{L, U}, {L, U}}]], (L + U)/2] yields (2 U)/(L - U)^2 (in V11.3), which is nonsense because when L and U are changed by any common addition the PDF should remain unchanged. – Coolwater Mar 23 at 21:00
• Maybe an inconsistency but not a bug. Instead of U if you pick any letter (a, b, c,...k, C, D,...,K) "below" L, then you end up with True. Choose any letter instead of U "above" L and you'll not get True. And don't use the bugs tag until you get confirmation from others that it is a bug. – JimB Mar 23 at 21:20
• Please read the description of the bugs tag before using it. – Michael E2 Mar 23 at 23:16
• @MarcoB While I'd certainly like to see it consistent, the "non-True" answer that the OP failed to produce is L == 0 || L + U != 2 t which is not False. So rather than "bug", I'd call it "not so desirable" or "inconvenient" in the scheme of things. – JimB Mar 24 at 1:59
• Unfortunately the lexical order of variable names affects the outcome of Simplify, FullSimplify and Reduce. This has be known for a long time. See this post from 2006. – m_goldberg Mar 24 at 3:04