Suppose that in any given time period a certain stock is equally likely to go up 11 unit or down 1 unit, and that the outcomes of different periods are independent. Let X₁ be the amount the stock goes up (either 1 or -1) in the first time period, and let Y be the cumulative amount it goes up in the first three periods. Find the correlation between X₁ and Y. (Hint: Let X, be the amount the stock goes up in the i-th time period so Y = X₁ + X₂ + X3.)

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