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

  1. #1
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    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
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  2. #2
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    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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