(a) The bivariate probability density function for X and Y denoted by f(x; y). Let f(x, y) equal x + y for (0 < equal to X < equal to 1) and (0 < equal to Y < equal to 1), zero otherwise. Find the marginal distributions for X and Y, respectively. Please denote them by fX(x) and fY (y).
(b) Using the same bivariate probability density function, find the covariance between X and Y .
(c) Continuing with the same definitions of X and Y, define W_1 = 6 + 12X + 24Y. Find the variance of W_1.
(d) Define W_2 = 12 + 12X - 24Y. Find the variance of W_2.
(e) Find the covariance between W_1 and W_2.
(f) Find the correlation coefficient between W_1 and W_2.