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.