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Characteristic function of an exponential distribution |
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| Mar10-05, 05:06 PM | #1 |
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Characteristic function of an exponential distribution
I need to calculate the characteristic function of an exponential distribution:
[tex] \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} [/tex] I have arrived at the following expression: [tex] \frac{{i\lambda }}{{i\lambda + t}}\mathop {\lim }\limits_{x \to \infty } \left( {e^{\left( {\lambda - it} \right)x} } \right) [/tex] and I can't calculate the limit. Any help would be appreciated. |
| Mar10-05, 06:08 PM | #2 |
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Nevermind this one, I had overlooked something in my calculations. I've solved it.
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