Is there anyone know Laplace transform? help me calculate value of $\displaystyle \mathbb E(exp(-\lambda X^2))$.
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And X is...?
Sorry, I make a missing: X~$\displaystyle N(\mu,\sigma^2)$
Then $\displaystyle X^2$ follows a chi-square distribution and you'll find the Laplace transform (mgf) on the Wikipedia page of the chi-square...
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