Hi everyone,

I have the following problem and I will be too happy to help me find a solution.
Consider a random variable
$$K_{ij}= \sum_{r=1}^N\sum_{c=1}^N W_{ir}W_{jc}=\sum_{r=1}^N\sum_{c=1}^N V^{ij}_{rc}$$
where $i \neq j$ and $W \in R$ are i.i.d. random variables $\mathcal{N}(0,1)$, my question is that I can claim $K_{ij}$ is the summation of **i.i.d. random variables**, I mean we can say that new random variables $V$ s are independent?
Thanks a lot in advance

notprimarily designed for making other people do the elementary level work for you (and neither is AoPS). Despite I often disagree with the official MO guidelines, this is a clear case when rereading them would be beneficial... – fedja Jun 2 '11 at 18:49