Variance of a combination of normal random variables
I have two normal random variables and such that both have zero mean and same standard deviation and I want to find out the variance of the random variable such that
where a and b are constants. I understand that is a normal random variable. So are and and that their product has a PDF given by modified bessel function of second kind. But how can I determine the variance of in terms of and .
Any help or pointers on this will be greatly appreciated. Thank you for your time.