Let X be N (0, 1)
(a) How do you find the p.d.f of |X|, a distribution that is often called the half normal?
(b) How do you find the expectation of |X| ?
Thank you for your time.
Well, is zero for all a. But, , which is enough to get the pdf by taking the derivative WRT x (note that, up to this point and after taking the derivative, we haven't used any information about the distribution of X). To find the expectation, just for simplicity let's set Y = |X| then find the expectation of Y in the usual way, now that we have the pdf for it. The function you need to integrate has an easy enough antiderivative.