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I'm referring to the article on Triangular Distribution, under the sub-heading: Distribution of the sum of two standard uniform variables.

Surely the maximum of sum of two uniform random numbers is not $1$. So $b$ needs to be $2$ and $c$ needs to be $1$ in the article. Am I missing something? I came across that article while writing my answer to this question, which has the correct solution.

Innocent
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The wiki page currently defines $X = \frac{X_1+X_2}{2}$ where $X_1,X_2$ are uniform on $[0,1]$, so $X$ is the mean, not the sum.

Maybe you're just arguing against the title of that subsection? It's entirely possible that it's a result of wikipedia having multiple authors.

Brian Moehring
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  • So should the correct title for that calculation be - "Distribution of the MEAN of two standard uniform variables"? – Innocent Feb 09 '20 at 11:01
  • It would arguably be more appropriate, yes. I don't know if I'd go as far as stating whether it's "correct". Scalar multiples are, after all, effectively equivalent except possibly in limiting cases. – Brian Moehring Feb 09 '20 at 11:05
  • Thanks, I just created a new account and submitted the edit. Lets see what the wiki mods say. – Innocent Feb 09 '20 at 11:05
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    @Innocent: There are no mods at Wikipedia. Wikipedia is edited collectively by all editors (now including you – welcome! :-). Your edit is fine; I'm sure it will stay. There was actually a previous incarnation of this section heading that said "mean"; it was changed to "Symmetric triangular distribution" in this edit, and later reintroduced as a sub-heading in this edit, now with "sum". – joriki Feb 09 '20 at 11:26
  • @joriki Thanks, I didnt know that, I somehow thought they followed same system as math.stackexchange. – Innocent Feb 09 '20 at 11:31