Explanation

Let's analyze each statement:

Statement A: "If a process is zero-mean white noise, then it must be Gaussian white noise."

• This is FALSE and the correct exception.
• Zero-mean white noise only requires the process to have zero mean, constant variance, and be serially uncorrelated.
• It does NOT require the distribution to be Gaussian/normal. White noise can follow other distributions (e.g., uniform, exponential, etc.).

Statement B: "If a process is Gaussian (aka, normal) white noise, then it must be (zero-mean) white noise."

• This is TRUE.
• Gaussian white noise implies the process is white noise (zero mean, constant variance, serially uncorrelated) AND normally distributed.

Statement C: "If a process is Gaussian (aka, normal) white noise, then it must be independent white noise."

• This is TRUE.
• For Gaussian processes, lack of correlation implies independence. Therefore, Gaussian white noise is automatically independent white noise.

Statement D: "If a process is stationary, has zero mean, has constant variance and it serially uncorrelated, then the process is white noise."

• This is TRUE.
• This is the standard definition of white noise: stationary process with zero mean, constant variance, and no serial correlation.

Therefore, the only false statement is A, making it the correct answer to "each of the following statements is true except."