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Oct 3, 2013 at 13:32 comment added jbowman To extend the answer slightly - the point about the limit is that it shows that the expectation is infinite for $\beta = 1$, as $\lim_{a \to \infty} \int_0^a x^{1-\beta}\text{d}x = \infty$. (Note since $x^- = 0$, technically $x$ has an infinite mean rather than not having a mean at all.)
Oct 3, 2013 at 12:12 history edited Glen_b CC BY-SA 3.0
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Oct 3, 2013 at 4:47 history edited Glen_b CC BY-SA 3.0
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Oct 3, 2013 at 4:37 history answered Glen_b CC BY-SA 3.0