Use partial fractions to integrate?
Let X be a randon variable with density function:
and
where c is such that this is a density.
Find
First I tried to take the integral of to find c, but I'm stuck here unless I get to use a calculator.
Are there anyway to find c? Or rather, do I need to find c in order to find the expected value, that is,
Oh, indeed !
Then if the moment exists... which is okay here since there's a continuous function in a compact.
So it doesn't work for the Cauchy distribution because the x*pdf near infinity is equivalent to 1/x, which is not integrable.
(hey I hate justifying things like that ^^)