n coin flips, X = # of heads, Y = # of tails
Cov(X,Y) = ?
X + Y = n
E[X]+E[y] = n
Therefore:
X-E[X] + y-E[Y] = 0
X-E[X]= -(y-E[Y])
$ Cov(X,Y)=-E[[X-E[X_ECE302Fall2008sanghavi]]^2]=-Var(X)=-Var(Y) $
and also the correlation coefficient is $ \rho(X,Y)=-1 $
