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## Main Question or Discussion Point

Is there a way to find the CDF of a random variable from its characteristic function directly, without first finding the PDF through inverse Fourier transform, and then integrate the PDF to get the CDFÉ

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Is there a way to find the CDF of a random variable from its characteristic function directly, without first finding the PDF through inverse Fourier transform, and then integrate the PDF to get the CDFÉ

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mathman

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Sorry, this isn't clear to me. Could you elaborate more? Where is ##x## in the integration to have ##F(x)##?

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mathman

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[tex]F(x)=\int_{-\infty}^{\infty}\frac{e^{-itx}}{-it}\phi(it)\,dt[/tex]

which is the IFT of ##\frac{\phi(it)}{-it}##?

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mathman

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∞

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