By "absolutely convergent," I assume that you mean that the integral converges for *any* subinterval of r ... and indeed, the antiderivative of rf(r)dr is ln(1 + r^2) / (2 * pi), which diverges on the interval [0, inf), for example.
Is there such a thing as a distribution for which the mean does exist but the variance (or second moment) does not? Or are those two always a "package deal?" |
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