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I have a uniform random variable $x$ and a normal random variable $z = \mathcal{N}(x, \sigma)$ (i.e. the mean is given by $x$). How can I draw samples $(X, Z)$ such that they correspond to their respective distributions? Can I draw from $x$ and $y = \mathcal{N}(0, \sigma)$ separately and then apply the transformation $z = x + y$?

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  • $\begingroup$ Yes - that should work. Personally, I write $Z \sim \mathcal{N}(x, \sigma^2)$ using the variance rather than the standard deviation $\endgroup$ – Henry Oct 22 '18 at 23:08

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