Hello everyone!

The question I have is:

and are indpt standard normal random variables, we have a random process ,where:

I would like to find out the distribution (one dimension FDD) of ,for a fixed

Here is what I did:

by Total Probability Formula

by independence

here is where I stuck...how should I deal with , or is there other ways to this kind of things?

What about n dimensional FDD?

Could anyone help me? :)