Variables and normal distributions

[ebrattr]

Hi everyone,
I would like to know if this stament is true or not. I have two variables $u,v$ both of them distributed as normal distribution with mean 0 and variance $a^2$. Is it true that the expected value of $uv$ is $a^2$ ?
Thanks

 

[mfb]

If u and v are independent, this is not true.
Just consider the symmetry of the system.

 

[ebrattr]

Yeahhh... its cero. Thanks.