In a piston assembly, the specifications for the clearance between piston rings and the cylinder wall are very tight. In a lot of assemblies, let Xbe the number with too little clearance and let Y be the number with too much clearance. The joint probability mass function of Xand Y is given in the table below: 0 0.15 0.12 0.11 0.10 1 0.09 0.07 0.05 0.04 2 0.06 0.05 0.04 0.02 3 0.04 0.03 0.02 0.01 a. Find the marginal probability mass function of X. b. Find the marginal probability mass function of Y. c. Are Xand Y independent? Explain. d. Find Ax and Ox e. Find tly, and Oy f. Find P(X + Y = 3) g. Find the conditional probability mass function pyx (y1) h. Find the conditional probability mass function pxly(x12) i. Find the conditional expectation E (Y|X = 1 j. Find the conditional expectation E(XY = 2)