the title essentially sums it up: let . My questions are:
1. Is there an analytical result for ?
2. If not, are there any appropriate approximations?
This question looks so innocent, I expect it must have been treated somewhere. I could, however, not find it in the relevant literature so far.
The variable transformation leads to (ignoring integration bounds)
So, my questions could also be interpreted as for the expectation of the random variable that is distributed according to a pdf that is proportional to . Unfortunately, I could not find any results for such a distribution, too.
Any help is greatly appreciated!