Understanding Stationary Noise: Expected Values and Variance

$X_t$ and $X_{t+τ}$ represent the random variable values of a signal at two different time points, while $μ_t$ and $μ_{t+τ}$ represent the expected values of the signal at those two time points. $σ$ represents the variance of the signal. For stationary noise, the variables at different time points follow the same distribution, with the same expected value and variance.