Let Xi~Ber(p) be independent random variables for i {1,2,3}. Let Y1=X1-X2, Y2=X2-X3, and Y3 = X3-X1.

a) Find the probability mass function for Y1

b)Find the Corr[Y1,Y2]

c)Find the joint probability mass function of Y1 and Y2.

d)The correlation matrix for Y1,Y2, and Y3 is the 3x3 matrix C, with Cij = Corr[Yi,Yj]. Find the eigenvalues of C. Can you make conjecture about the eigenvalues of any correlation matrix