Determine the Laplace transform (hat{f}(s)) of the density of the Laplace distribution with parameters (lambda) and (mu):

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Determine the Laplace transform \(\hat{f}(s)\) of the density of the Laplace distribution with parameters \(\lambda\) and \(\mu\):

\[f(x)=\frac{1}{2} \lambda e^{-\lambda|x-\mu|}, \quad-\infty

By means of \(\hat{f}(s)\) determine \(E(X), E\left(X^{2}\right)\), and \(\operatorname{Var}(X)\).

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