# Math Help - Finding the Characteristic Function of a Standard Laplace Distribution

1. ## Finding the Characteristic Function of a Standard Laplace Distribution

How do you find the Characteristic Function of a Standard Laplace Distribution:

Let X denote a real-valued random variable with an absolutely continuous distribution with density function p(x) = $\frac{1}{2}$ $e^{-|x|}$, $\hspace{5mm}$- $\infty$< x < $\infty$.

Find the characteristic function.

Attempt:

I know that the setup should look something like this:

$\frac{1}{2}$ $\int_{-\infty}^\infty$ $e^{itx}$ $e^{-|x|}$dx

2. ## Re: Finding the Characteristic Function of a Standard Laplace Distribution

Hey ishihara.

You should evaluate two integrals: one for (-infinity,0) and one for [0,infinity) by replacing |x| with -x on first integral and +x on second integral. Also recall that Integral e^(ax) = (1/a)*e^(ax) + C (indefinite integral that is).