If two random variables X and Y are such that $$E(X)+E(Y)=0\dots, \tag1$$ $Var(X)=Var(Y)$ and $1+r=0$ where $r$ is the correlation co-efficient between $X$ and $Y$,then what is the relation between $X$ and $Y$?[E(x) is the expectation of X]
I do not really know how to proceed. This is all that I could gather:
$Var(X)=Var(Y)\implies E(X^2)-E^2(X)=E(Y^2)-E^2(Y)$ which means that $E(X^2)=E(Y^2)$ on account of $(1)$.
From the other condition I get $r=-1$ ie.e $E(XY)-E(X)E(Y)=-Var(X)=-Var(Y)$.
But after that I seem lost;can anyone please point out how I can establish a relation between $X$ and $Y$?