Answer-first summary for fast verification
Answer: If a process is zero-mean white noise, then it must be Gaussian white noise.
## 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.
Author: LeetQuiz Editorial Team
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In regard to white noise, each of the following statements is true except?
A
If a process is zero-mean white noise, then it must be Gaussian white noise.
B
If a process is Gaussian (aka, normal) white noise, then it must be (zero-mean) white noise.
C
If a process is Gaussian (aka, normal) white noise, then it must be independent white noise.
D
If a process is stationary, has zero mean, has constant variance and it serially uncorrelated, then the process is white noise.
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