probability distribution with infinite variance but finite mean - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-05-24T01:38:49Z http://mathoverflow.net/feeds/question/75798 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/75798/probability-distribution-with-infinite-variance-but-finite-mean probability distribution with infinite variance but finite mean gustavolacerda 2011-09-18T23:59:13Z 2011-09-19T01:37:29Z <p>Does such a distribution exist? The Cauchy distribution has infinite variance but its mean is also undefined.</p> http://mathoverflow.net/questions/75798/probability-distribution-with-infinite-variance-but-finite-mean/75802#75802 Answer by Steven Landsburg for probability distribution with infinite variance but finite mean Steven Landsburg 2011-09-19T00:29:36Z 2011-09-19T00:29:36Z <p>Consider the density function \$f(x)= (3/2) x^{-5/2}\$ on the interval from \$1\$ to infinity.</p> <p>More generally, Google for the term "Pareto distribution".</p> http://mathoverflow.net/questions/75798/probability-distribution-with-infinite-variance-but-finite-mean/75808#75808 Answer by Michael Hardy for probability distribution with infinite variance but finite mean Michael Hardy 2011-09-19T01:37:29Z 2011-09-19T01:37:29Z <p>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.</p>