A random variable has cdf of the form , is real, is real and .
Find the pdf function of .
Find the form of the moment generating function and hence calculate the variance of
[Note : the gamma function, is such that .
The pdf turns out to be .
Using the fact that if then ,
It turns out that
We then have which, according to Maple, is equal to .
But then I end up with dividing by zero errors when trying to calculate .
Plus I don't see how nor where to use the note given in the exercice.
Any help would be much appreciated. Thank you.