1. Your father knows that last week you have learned jointly distributed random variables from Aybek Hoca. He has asked you to calculate certain distributions and expectations. Please let X denote the amount of pepper in the kitchen on an "ordinal" scale. Respectively the values of X {-1,0,1,2} denote non-existence, scanty amount, satisfying amount and full. Further- more, please let Y denote the amount of salt in the kitchen. Y = 1 indicates there is salt, Y = -1 shows there are none. The joint distribution may be observed below based on your father's observations. Table 1: Joint Distribution X \Y -1 1 -1 0.2 0.1 0 0.1 0.1 1 0.3 0.1 21 0.05 0.05 a) Please help him comprehend the marginal distributions of X and Y. b) Are X and Y independently distributed? c) Please calculate E[X], E[Y], letting g(x, y) = xy, E[g(x, y)] d) He tells you that if there is no salt in the kitchen, how much pepper in terms of the scales we have defined should he expect to see? (E[Y|X = 2], or not?)