51. Let X and Y each take on either the value 1 or - 1 . Let

ñ(\91) = Ñ[×= 1,7 = 1}, P(\,-\) = P{X= i , y = - i ) f p(-\y\) = P[X=-UY= 1},

ñ(-\,-1) = Ñ[×=-\9Õ=-\}

Suppose that E[X] = E[Y] = 0. Show that

(a) / ? ( l , l ) = / ? ( - l , - l )

(b) p(U-l)=p(-U\)

Let ñ = 2/7(1, 1). Find

(c) Var(*)

(d) Var(r)

(e) Cov(X,Y)