8. (20 pts) The joint probability mass function of X and Y is given by px,Y(1, 1) = 0.2, px,Y(1, 2) = 0.4, px,Y(2, 1) = 0.3, px,Y (2, 2) = 0.1 Find the each of the following. Give exact answers using fraction or decimal. a. Compute the marginal distribution Px (i), Py (i), i = 1,2 b. Compute the conditional distribution of X given Y, PxIY(ilj), i = 1,2; j = 1,2 c. Compute the conditional distribution of Y given X, Prix (ilj), i = 1,2; j = 1,2 d. Are X and Y independent? Why