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Characteristic function of an exponential distribution

  1. Mar 10, 2005 #1
    I need to calculate the characteristic function of an exponential distribution:
    \phi _X \left( t \right) = \int\limits_{ - \infty }^\infty {e^{itX} \lambda e^{ - \lambda x} dx} = \int\limits_{ - \infty }^\infty {\lambda e^{\left( {it - \lambda } \right)x} dx}

    I have arrived at the following expression:
    \frac{{i\lambda }}{{i\lambda + t}}\mathop {\lim }\limits_{x \to \infty } \left( {e^{\left( {\lambda - it} \right)x} } \right)

    and I can't calculate the limit.
    Any help would be appreciated.
  2. jcsd
  3. Mar 10, 2005 #2
    Nevermind this one, I had overlooked something in my calculations. I've solved it.
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