Questions: Two variables are said to display correlation if - both measure the same thing. - one occurs before the other. - they are caused by the same factor. - they vary together.

Solution Steps

The covariance between the variables \( X \) and \( Y \) is calculated as follows:

\[ \text{Cov}(X,Y) = 5.0 \]

The standard deviations of \( X \) and \( Y \) are given by:

\[ \sigma_X = 1.58 \] \[ \sigma_Y = 3.16 \]

The correlation coefficient \( r \) is computed using the formula:

\[ r = \frac{\text{Cov}(X,Y)}{\sigma_X \sigma_Y} \]

Substituting the values:

\[ r = \frac{5.0}{1.58 \times 3.16} = 1.0 \]

Final Answer