combine the exponents of e, you need to complete the square
This can be found in many books.
It's a bit messy but it works.
I'm stuck with something that I think should be straightforward but can't see what to do.
I'm trying to find where ~N( , ). I know that this is i.e. the integral of the inner product of and the pdf of the Normal distribution. This is where it falls apart - how do I integrate this? I think it's done by substitution when dealing with with the standard normal but this has the extra exponential and I'm not sure how to do it.
Help appreciated, thanks.
Thanks for the reply.
Combining and and then completing the square I get .
I think the idea is to now split this into and and then take the latter outside of the integral.
This leaves me with but I still can't solve this even with a change of variable as it doesn't converge. Am I missing something or is this the wrong idea?