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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x is a dummy variable. Integrate the expression for f(x) (pdf) from a to b to and then switch the order of integration to get the expession I presented. The important thing is that the same expression holds for the even when you don't have a pdf. If you want F(x), let b=x and see if a going to [tex]-\infty[/tex] makes sense.