Answer: 0.00148

**Step-by-step solution:** 1. **Given values:** - Correlation between X and Y, ρ(X,Y) = 0.50 - Standard deviation of Y, σᵧ = 0.26 - Covariance between X and Y, Cov(X,Y) = 0.005 - We need to find variance of X, Var(X) = σₓ² 2. **Correlation formula:** ρ(X,Y) = Cov(X,Y) / (σₓ × σᵧ) 3. **Substitute known values:** 0.50 = 0.005 / (σₓ × 0.26) 4. **Solve for σₓ:** σₓ × 0.26 = 0.005 / 0.50 σₓ × 0.26 = 0.01 σₓ = 0.01 / 0.26 σₓ = 0.0384615 ≈ 0.0385 5. **Calculate variance of X:** Var(X) = σₓ² = (0.0385)² = 0.00148225 ≈ 0.00148 **Key points:** - Correlation is the standardized covariance - Variance is the square of standard deviation - The calculation requires solving for the unknown standard deviation first, then squaring it to get variance - Option C (0.0385) is the standard deviation, not the variance - Option D (0.0148) is off by a factor of 10 - Option A (0.13) is incorrect

Author: Nikitesh Somanthe