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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 ( σ ) is:
      r = Cov(X, Y) / ( σ ₓ * σ ᵧ )
      We need to find Cov(X, Y). Rearranging the formula:
      Cov(X, Y) = r * σ ₓ * σ ᵧ
      Given: r = -0.8, σ ₓ = 4, σ ᵧ = 5.
      Cov(X, Y) = (-0.8) * (4) * (5)
      Cov(X, Y) = (-0.8) * 20 =  -16 .

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