If X is a normal random variable with mean and variance , show that:
aha!
its easier than i thought. make that substitution and you will get an integral you can actually evaluate directly.
we started from
sub
so
To get
you can evaluate that integral using standard methods. hopefully the right answer drops out!
(reminder: and
edit i did it to check:
Evaluating the integral gives
Which simplifies to the required answer.
phew!
not bad for an economist, if i do say so myself....even if it took about 10 tries