Variables and normal distributions

ebrattr
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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
 
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If u and v are independent, this is not true.
Just consider the symmetry of the system.
 
Yeahhh... its cero. Thanks.
 

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