I have problems when I get the integral $$\int_{0}^{\infty}\frac{e^{-(\frac{x^{2}}{2u}+u)}}{\sqrt{u2\pi}} du$$ what should I do? Or this result is wrong?
2026-04-05 22:36:24.1775428584
If $X|\Sigma^{2}=u\sim N(0,u)$ with $\Sigma^{2}\sim exp(1)$ Find the density of X.
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