Final answer:
The sequence x(n) is a zero-mean Gaussian sequence with a standard normal distribution and is WSS. The derived sequence y(n) does not maintain independence due to the dependence on previous terms and is not WSS, but still has a zero mean.
Step-by-step explanation:
The random sequence x(n) is a zero-mean uncorrelated Gaussian random sequence with variance σ2(n)=1. This means that each element in the sequence, x(n), follows a standard normal distribution, denoted as X ~ N(0, 1). Being uncorrelated implies that no element in the sequence is linearly related to another, and because it has a constant mean and variance, it is considered to be Wide Sense Stationary (WSS).
For the derived sequence y(n), which is defined as y(n) = x(n) − x(n − 1), the independence between elements does not hold because each element depends on the previous one. The mean of y(n) is still zero, as it is the difference of two variables with zero mean. To characterize the auto-correlation of y(n), one would need to consider the correlation between the differenced terms, which are not independent. However, y(n) is not WSS due to the dependence on previous elements.