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%.