Explanation

This question appears to be incomplete as it only shows statement IV and the answer choices, but not statements I, II, and III. However, based on the pattern and typical content in quantitative analysis, I can analyze what we have:

Statement IV: "The product of two independent random lognormal variables is also a random lognormal variable."

This statement is TRUE. For lognormal variables:

• If X ~ Lognormal(μ₁, σ₁²) and Y ~ Lognormal(μ₂, σ₂²) are independent
• Then ln(X) ~ N(μ₁, σ₁²) and ln(Y) ~ N(μ₂, σ₂²)
• The product XY has ln(XY) = ln(X) + ln(Y) ~ N(μ₁ + μ₂, σ₁² + σ₂²)
• Therefore, XY ~ Lognormal(μ₁ + μ₂, σ₁² + σ₂²)

Answer Analysis:

• Option C (III and IV only) would be correct if statement III is also true
• Without seeing statements I, II, and III, I cannot definitively determine the correct answer
• However, based on the structure and typical FRM questions, statement IV is correct

Note: The question appears to be missing the complete set of statements I, II, III, and IV that would normally precede the answer choices.