Having (rather foolishly) involved myself into providing an answer for Cross Validated: “Can the standard deviation of non-negative data exceed the mean?“, I ended up having to derive the mean of the absolute value of a Student’s variate X. (Well, not really, but then I did.) I think the following is correct: where is the 
Zero Inflated Models and Generalized Linear Mixed Models with R.
Zuur, Saveliev, Ieno (2012).
