Question: Let X and Y be random variables with the space consisting of the four points (0, 0), (1, 1), (1, 0), (1,1). Assign positive probabilities

Let X and Y be random variables with the space consisting of the four points (0, 0), (1, 1), (1, 0), (1,−1). Assign positive probabilities to these four points so that the correlation coefficient is equal to zero. Are X and Y independent?

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