Question: 2. (a) If two random variables X and Y are independent, then E[XY] = E[X]ELY]. However, the reverse implication does not hold: if E[XY] =

2. (a) If two random variables X and Y are independent, then E[XY] = E[X]ELY]. However, the reverse implication does not hold: if E[XY] = E[X]E[Y], then Y and X are not necessarily independent. Consider for example the sample space 0 = {-3, -2, -1, 0, 1, 2, 3} equipped with the uniform measure (i.e., P(i) = = for all -3

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