I'm in the process of finding $E(XY)$ where X and Y are non-independent Bernoulli random variables with both of them with probability of $\frac{n}{N}$
I understand that $E(XY)=\Sigma\Sigma x_{i}y_{i}P(X,Y)$ and this got me to the point where I can write: $E(XY)=P(X=1,Y=1)\cdot1+P(X=1,Y=0)\cdot0+P(X=0,Y=1)\cdot0+P(X=0,Y=0)\cdot0$ $=P(X=1,Y=1)$
But Im very lost here. Some help would be appreciated.
This is correct. It's just equal to the probability that both RVs take a value of 1, which is equal to the product of the parameters if they are independent, and some other number that might be given otherwise.