- #1

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## Main Question or Discussion Point

so a charateristic function of a RV is complex valued funtion. from my lecture, the distribution funtion of a Random variable is not always "well behaved", may not have a density etc. A charateristic function on the other had is "well behave".

What i dont understand is, is that the only reason we use it ?

how is it actually derived, why does it have to be complex valued .

this is the definition i'm given [tex] \phi(t) = \mathbb{E}(e^{itX})[/tex]

how is this actually derived, is somewhere where i can find the proof ?

What i dont understand is, is that the only reason we use it ?

how is it actually derived, why does it have to be complex valued .

this is the definition i'm given [tex] \phi(t) = \mathbb{E}(e^{itX})[/tex]

how is this actually derived, is somewhere where i can find the proof ?