mean value of a correlated variables product

I everybody,

I have a problem and I was thinking if somebody could help me;

I have to calculate the mean value

per

where and are two samples of the same process y which is gaussian with 0 mean and known sqare value .

The problem is that the correlation of the process is exponential:

;

I believe I should calculate the joint probability density function but I don't know how.

Please could somebody help me, or simply tell me a good reference where I can find this topic?

Thanks a lot.