Answer: 0.22

## Explanation The correlation coefficient is calculated using the formula: \[ \rho_{X,Y} = \frac{\text{Cov}(X,Y)}{\sigma_X \cdot \sigma_Y} \] From the covariance matrix: - Variance of X = 650, so standard deviation σ_X = √650 = 25.50 - Variance of Y = 450, so standard deviation σ_Y = √450 = 21.21 - Covariance between X and Y = 120 Now calculate: \[ \rho_{X,Y} = \frac{120}{25.50 \times 21.21} = \frac{120}{540.855} = 0.2218 \approx 0.22 \] Therefore, the correlation coefficient is approximately 0.22. **Key points:** 1. The diagonal elements of a covariance matrix represent variances 2. Off-diagonal elements represent covariances 3. Correlation is the standardized covariance (covariance divided by the product of standard deviations) 4. Correlation values range from -1 to +1

Author: Nikitesh Somanthe