# Expected value of two dependent Bernoulli random variables.

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.

• $X$ and $Y$ are both Bernoulli random variable with same probability of success. So $P(X=1)=P(Y=1)=p$ Nothing much is given to be honest. – Ya G Feb 16 '17 at 3:57
• You have correctly identified $\mathsf E(XY)=\mathsf P(X=1,Y=1)$. We cannot proceed because we do not know what this joint probability may be. Your post has specified that the variables are not independent yet not indicated what dependency they do have. – Graham Kemp Feb 16 '17 at 9:08