Hi everybody,
I attached a pdf file with an exercise (moment generating function). I dont understand two steps which are described in this file.
I would be very glad if someone could help.
Many thanks,
Fab
Hi everybody,
I attached a pdf file with an exercise (moment generating function). I dont understand two steps which are described in this file.
I would be very glad if someone could help.
Many thanks,
Fab
You need to know these 2 facts to follow this answer:
- (if r is an integer)
Answer
move 1 power of "a" outside the fraction
=
multiply top and bottom by
=
=
substitute v=ax, noting that
=
=
move constants outside the integral
=
The integral is now in the same form as the definition of the gamma function. i haven't written the limits in but they are still 0 and infinity, as required.
=
now (since r is in integer) we can use this property of the gamma function:
=>
note that
=>
=