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1 vote

Can an unskewed distribution be expressed as product of a normal and another distribution?

The characteristic function of $x$ is $\varphi(s) = \mathbb E[e^{isx}] = \mathbb E[e^{-s^2 y^2/2}]$. The fact that $\varphi(s) \to 0$ as $s \to \pm \infty$ tells you that $x$ is continuous.
Robert Israel's user avatar