Let $X_1,X_2$ be i.i.d $N(0,\sigma^2)$.
My tasks is to calculate the expected value of the function $T=|X_1-X_2|$.
Intuitively, I want to say that this value would equal the standard deviation, but I sort of doubt that this is the case because the standard deviation is the expected distance from the mean, and not just any observation... Any ideas?
