Let x and y have the joint pmf described as follows: (x, y) (1, 1) (1, 2) (1, 3) (2, 1) (2, 2) (2, 3) p(x, y) 2 15 4 15 3 15 1 15 1 15 4 15 and p(x, y) is equal to zero elsewhere.
(a) find the means μ1 and μ2, the variances σ2 1 and σ2 2, and the correlation coefficient rho.
(b) compute e(y |x = 1), e(y |x = 2), and the line μ2 + rho(σ2/σ1)(x − μ1). do the points [k, e(y |x = k)], k = 1, 2, lie on this line?