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      Question

      If the Correlation Coefficient (r) between two variables

      X and Y is -0.8, and their standard deviations are 4 and 5 respectively, the covariance between X and Y is:
      A -16 Correct Answer Incorrect Answer
      B 16 Correct Answer Incorrect Answer
      C -0.64 Correct Answer Incorrect Answer
      D -13.2 Correct Answer Incorrect Answer
      E 0.64 Correct Answer Incorrect Answer

      Solution

      • The formula connecting Correlation Coefficient (r), Covariance (Cov), and Standard Deviations ( Οƒ ) is:
        r = Cov(X, Y) / ( Οƒ β‚“ * Οƒ ᡧ )
        We need to find Cov(X, Y). Rearranging the formula:
        Cov(X, Y) = r * Οƒ β‚“ * Οƒ ᡧ
        Given: r = -0.8, Οƒ β‚“ = 4, Οƒ ᡧ = 5.
        Cov(X, Y) = (-0.8) * (4) * (5)
        Cov(X, Y) = (-0.8) * 20 =Β  -16 .

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