Geodesic
Remarks on Uncorrelated Gaussian Dependent Random Variables
Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 1, pp. 141-143

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Formula (3) of the present paper gives a general example of two uncorrelated Gaussian dependent random variables with non-Gaussian joint distribution. In this formula $\varphi(x)$ is a bounded even real valued function defined on the real line such that $\frac1{\sqrt{2\pi}}\int_{-\infty}^\infty\varphi(x)e^{-x^2/2}\,dx=0$, $h$ is equal to $\sup_{-\infty$ and $-1\le\lambda\le1$. 
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     author = {O. V. Sarmanov},
     title = {Remarks on {Uncorrelated} {Gaussian} {Dependent} {Random} {Variables}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {141--143},
     publisher = {mathdoc},
     volume = {12},
     number = {1},
     year = {1967},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1967_12_1_a14/}
}
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O. V. Sarmanov. Remarks on Uncorrelated Gaussian Dependent Random Variables. Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 1, pp. 141-143. http://geodesic.mathdoc.fr/item/TVP_1967_12_1_a14/