Answer: Mean = $400,000; variance = $800,000

## Explanation For a chi-square distribution with n degrees of freedom: - Mean = n - Variance = 2n Given that X follows a chi-square distribution with 2 degrees of freedom: - Mean of X = 2 (in units of $100,000) - Variance of X = 4 (in units of $100,000) Since the two projects are independent: - Mean of total loss = E(X₁ + X₂) = E(X₁) + E(X₂) = 2 + 2 = 4 (in units of $100,000) - Variance of total loss = Var(X₁ + X₂) = Var(X₁) + Var(X₂) = 4 + 4 = 8 (in units of $100,000) Converting to dollars: - Mean = 4 × $100,000 = $400,000 - Variance = 8 × $100,000 = $800,000 Alternatively, the sum of two independent chi-square variables with 2 degrees of freedom each gives a chi-square variable with 4 degrees of freedom: - Mean = 4 (in units of $100,000) = $400,000 - Variance = 2 × 4 = 8 (in units of $100,000) = $800,000 Thus, option D is correct: Mean = $400,000; Variance = $800,000.

Author: Nikitesh Somanthe