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I have two independent random variables $x$ and $y$.

Let's assume that y follows a standard normal distribution, $N(0,1)$

I want some results that $xy\~N(a,b)$ (e.g. $a=0$ and $b=1$)

Which distribution $x$ should follow to get Gaussian distribution random variable, $xy$?

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    $\begingroup$ Are $X$ and $Y$ supposed to be independent? $\endgroup$ Commented Mar 18, 2020 at 11:59
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    $\begingroup$ Make $X$ a constant. $\endgroup$ Commented Mar 18, 2020 at 12:09
  • $\begingroup$ Yes, X and Y are independent $\endgroup$ Commented Mar 19, 2020 at 0:42

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