Answer: I only

## Explanation Let's analyze each statement: **Statement I**: "The sum of two independent random normal variables is also an independent random normal variable." - **TRUE**: This is a fundamental property of normal distributions. If X ~ N(μ₁, σ₁²) and Y ~ N(μ₂, σ₂²) are independent, then X + Y ~ N(μ₁ + μ₂, σ₁² + σ₂²). **Statement II**: "The product of two random normal variables is also a random normal variable." - **FALSE**: The product of two normal variables is NOT normally distributed. In fact, the product follows a more complex distribution (related to the Bessel function). **Statement III**: "The sum of two random lognormal variables is also a random lognormal variable." - **FALSE**: The sum of lognormal variables is NOT lognormal. Lognormal distributions are closed under multiplication, not addition. Therefore, only Statement I is true, which corresponds to option A.

Author: LeetQuiz Editorial Team