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Henry.L
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gradstudent
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Looking for a certain kind of a distribution

Is there any probability distribution supported on a compact or a half-open interval (of $\mathbb{R}$) such that if a vector $\vec{x} \in \mathbb{R}^n$ is sampled by sampling its coordinates like that then there is a closed form expression for the distribution of $\langle \vec{a} , \vec{x}\rangle$ (as a function of $\vec{a}$)?


The closest example I know of is the Gaussian distribution which is supported on the whole of $\mathbb{R}$.