1. Your father knows that last week you have learned jointly distributed random variables from Aybek Hoca. He has asked you to calculate certain
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?)
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