Explanation

Let's analyze each statement:

Statement A: FALSE

• Zero-mean white noise does NOT necessarily imply Gaussian white noise
• White noise can have various distributions (uniform, exponential, etc.) as long as it has zero mean, constant variance, and no serial correlation
• Gaussian white noise is a specific case where the distribution is normal

Statement B: TRUE

• Gaussian white noise by definition has zero mean, constant variance, and no serial correlation
• Therefore, it satisfies the definition of white noise

Statement C: TRUE

• Gaussian white noise implies independence (not just uncorrelated)
• For Gaussian processes, uncorrelated implies independent

Statement D: TRUE

• This is the standard definition of white noise: stationary, zero mean, constant variance, and serially uncorrelated

Therefore, statement A is the incorrect one as zero-mean white noise does not necessarily have to be Gaussian.