Answer: 0.0338.

## Explanation To calculate covariance from correlation coefficient and variances, we use the formula: **Covariance (σ₁₂) = Correlation coefficient (ρ) × Standard deviation of Stock 1 (σ₁) × Standard deviation of Stock 2 (σ₂)** **Step 1: Calculate standard deviations** - Standard deviation of Stock 1 = √(Variance of Stock 1) = √0.0625 = 0.25 - Standard deviation of Stock 2 = √(Variance of Stock 2) = √0.0900 = 0.30 **Step 2: Calculate covariance** - Covariance = 0.4500 × 0.25 × 0.30 - Covariance = 0.4500 × 0.075 - Covariance = 0.03375 ≈ 0.0338 **Verification:** - Option A (0.0025) is too small - this would be the product of the variances (0.0625 × 0.0900 = 0.005625), not the covariance - Option B (0.0338) is correct - Option C (0.0675) is double the correct value **Key Concept:** The correlation coefficient (ρ) measures the strength and direction of the linear relationship between two variables, scaled between -1 and +1. Covariance measures the joint variability of two random variables but is not standardized. The relationship is: ρ = σ₁₂ / (σ₁ × σ₂), where σ₁₂ is covariance, σ₁ is standard deviation of Stock 1, and σ₂ is standard deviation of Stock 2.

Author: LeetQuiz .