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![\mathbb{E}[|X|]=\mu(2\text{P}_{\mu,\nu}(X>0)-1)\qquad\qquad\\ \qquad\qquad+2 f(0,\nu)\dfrac{\nu}{\nu-1}\left[1+\mu^2/\nu\right]^{-(\nu-1)/2}](http://s0.wp.com/latex.php?latex=%5Cmathbb%7BE%7D%5B%7CX%7C%5D=%5Cmu(2%5Ctext%7BP%7D_%7B%5Cmu,%5Cnu%7D(X%3E0)-1)%5Cqquad%5Cqquad%5C%5C+%5Cqquad%5Cqquad+2+f(0,%5Cnu)%5Cdfrac%7B%5Cnu%7D%7B%5Cnu-1%7D%5Cleft%5B1+%5Cmu%5E2/%5Cnu%5Cright%5D%5E%7B-(%5Cnu-1)/2%7D&bg=000000&fg=B0B0B0&s=0 "\mathbb{E}[|X|]=\mu(2\text{P}_{\mu,\nu}(X>0)-1)\qquad\qquad\\ \qquad\qquad+2 f(0,\nu)\dfrac{\nu}{\nu-1}\left[1+\mu^2/\nu\right]^{-(\nu-1)/2}")
where
&bg=000000&fg=B0B0B0&s=0 "f(x,\nu)")
Filed under: R, Statistics, University life Tagged: absolute t distribution, cross validated, folded t distribution, moment derivation
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