Q3 X and Y are discrete random variables with joint distribution as follows: X = 0 X=1 X=3 Y = -1 0.08 0.03 0.00 Y=0 0.03 0.12 0.20 Y=3 0.11 0.11 0.06 Y = 4.5 0.04 0.20 0.02 (i) (a) Identify which one of the following options gives the correct value of the expectation E(Y|X = 1): [2] (A1) 1.3789 (A2) 2.6087 (A3) 3.1398 (A4) 4.0945 (b) Identify which one of the following options gives the correct value of the variance var(XY = 3): [2] (A1) 1.2487 (A2) 0.9832 (A3) 1.9388 (A4) 2.2235 3 (ii) Calculate the probability functions of the marginal distributions for X and Y. [2] (iii) Determine whether X and Y are independent. 121