Answer: Mean = 0.45, variance = 0.38

## Explanation This is a **binomial distribution** problem: - **n = 3** bonds - **p = 0.15** (default probability for each bond) - Default events are **independent** **Mean calculation:** - Mean = n × p = 3 × 0.15 = **0.45** **Variance calculation:** - Variance = n × p × (1 - p) = 3 × 0.15 × 0.85 = 0.3825 ≈ **0.38** **Verification:** - Option B: Mean = 0.45, variance = 0.38 ✓ - Option A: Mean too small (0.15), variance incorrect - Option C: Mean correct but variance too small (0.32) - Option D: Mean too small (0.15), variance incorrect The number of defaults follows a Binomial(3, 0.15) distribution, with mean 0.45 and variance 0.3825.

Author: LeetQuiz Editorial Team