I am looking for some distributional characteristic (for example a characteristic function) of a random variable which is defined as $aX+bX^2+cX^3$, where $X$ is a standard normal variable. Is there some way to approach this problem?
Thanks!
2026-03-30 06:47:27.1774853247
Distribution of $aX+bX^2+cX^3$ where $X$ is standard normal
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