Answer: The conditional one-year default probability, given survival through the first year, is 17.3%

## Explanation With a constant hazard rate λ = 0.090: **A. Unconditional one-year default probability:** - P(default in year 1) = 1 - e^(-λ) = 1 - e^(-0.090) = 1 - 0.9139 = 0.0861 = 8.61% ✓ **B. Unconditional two-year default probability:** - P(default within 2 years) = 1 - e^(-2λ) = 1 - e^(-0.180) = 1 - 0.8353 = 0.1647 = 16.47% ✓ **C. Joint probability of survival through year 1 and default in year 2:** - P(survive year 1) = e^(-λ) = 0.9139 - P(default in year 2 | survive year 1) = 1 - e^(-λ) = 0.0861 - Joint probability = 0.9139 × 0.0861 = 0.0787 = 7.87% ✓ **D. Conditional one-year default probability given survival through first year:** - This should be equal to the hazard rate λ = 0.090 = 9.0% - The statement says 17.3%, which is incorrect ✗ The false statement is D because the conditional default probability given survival through the first year equals the hazard rate (9.0%), not 17.3%.

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