Integral in 1 is just a sum of integral over log-normal density and integral which is reduced (by introducing new variable =( log(x)-mu )/ sigma ) to integral over odd function which equals to zero
Hello math minds,
This is my first post. I was over at physics forums (under a different name) but have quickly migrated to this site after finding it .
I would appreciate it if someone could walk me through this, if like me, you find yourself with a lot of free time.
Let be a random variable with probability density function
and (a piecewise function) where are parametres (N and R denote natural and real numbers). Note that when is the pdf corresponding to a long-normal distribution.
(1) Show that
(2) Show that the moments for all do not depend on or n.
(3) Show that is infinite for any t > 0
Good Luck
Integral in 1 is just a sum of integral over log-normal density and integral which is reduced (by introducing new variable =( log(x)-mu )/ sigma ) to integral over odd function which equals to zero