# Question

n coin flips, X = # of heads, Y = # of tails

Cov(X,Y) = ?

=Answer+ 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 $