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Aug 1, 2017 at 22:55 comment added Henry.L @gradstudent You are basically projecting the folded normal $vec{x}$ onto the direction defined by $\vec{a}$
Aug 1, 2017 at 22:51 comment added gradstudent Thanks! Could you share your intuition about why you think the PDF of $\langle \vec{a}, \vec{x} \rangle$ has a closed form expression with coordinates of $\vec{x}$ coming from say the folded normal?
Aug 1, 2017 at 22:39 history answered Henry.L CC BY-SA 3.0