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About LinkBacksLet 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.
question about a "half normal" distribution? Thanks for checking this out.
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.
Hint:Originally Posted by Intsecxtanx
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.if
and zero otherwise.
Second hint: Normals are symmetric about their mean.
After you find the pdf integrate to find the expectation. If you need help with that, post here.
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.
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