May be
Maybe the 1917 Cantelli conjecture? If $f$ is a positive function on real numbers, if $X$ and $Z$ are $N(0,1)$ independent rv such that $X+f(X)Z$ is normal, prove that $f$ is a constant ae.
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May be the 1917 Cantelli conjecture? If $f$ is a positive function on real numbers, if $X$ and $Z$ are $N(0,1)$ independent rv such that $X+f(X)Z$ is normal, prove that $f$ is a constant ae. |
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