# Thread: 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) = $\displaystyle \frac{1}{2}$$\displaystyle e^{-|x|}, \displaystyle \hspace{5mm}-\displaystyle \infty < x < \displaystyle \infty. Find the characteristic function. Attempt: I know that the setup should look something like this: \displaystyle \frac{1}{2}$$\displaystyle \int_{-\infty}^\infty$$\displaystyle e^{itx}$$\displaystyle 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).

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# solution of characteristic function of standard laplace distribution

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