1. use Laplace transform

Is there anyone know Laplace transform? help me calculate value of $\mathbb E(exp(-\lambda X^2))$.

And X is...?

3. Re: use Laplace transform

Sorry, I make a missing: X~ $N(\mu,\sigma^2)$

4. Re: use Laplace transform

Then $X^2$ follows a chi-square distribution and you'll find the Laplace transform (mgf) on the Wikipedia page of the chi-square...