Does such a distribution exist? The Cauchy distribution has infinite variance but its mean is also undefined.
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closed as off topic by Andreas Blass, Gerald Edgar, Deane Yang, Will Jagy, George Lowther Sep 19 2011 at 1:50 |
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Consider the density function $f(x)= (3/2) x^{-5/2}$ on the interval from $1$ to infinity. More generally, Google for the term "Pareto distribution". |
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In addition to the Pareto distribution for suitable parameter values, the t-distribution has a mean of 0 if the number of degrees of freedom is more than 1, but has infinite variance if it is not more than 2. |
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