For a Wide-Sense Stationary (WSS) process $X(t)$ with autocorrelation function $R(\tau)$, the second moment of $X(t)$ at any specific time $t = 3$ (or any $t$ in general) is the expected value of the square of $X(3)$, which can be expressed as $E[X(3)^2]$.

In the context of a WSS process, the second moment $E[X(3)^2]$ is equivalent to the autocorrelation function evaluated at zero time lag because WSS processes have constant mean and variance over time. Thus, we have:

$E[X(3)^2] = R(0)$

where $R(0)$ is the autocorrelation at zero lag, which represents the variance of the process $X(t)$.

So, to find the second moment of $X(3)$, you simply need $R(0)$.

Summary:

The second moment of $X(3)$ for a WSS process is $R(0)$, the value of the autocorrelation function at $\tau = 0$.

Would you like further details on how autocorrelation functions relate to second moments or have additional questions?

Here are related questions that might interest you:

1. How does the mean of a WSS process affect its autocorrelation function?
2. What is the significance of $R(\tau)$ for different values of $\tau$?
3. How does stationarity impact the properties of a random process?
4. Can we determine $R(\tau)$ if we only know the second moment $E[X(3)^2]$?
5. How do we compute $R(\tau)$ for a given WSS process with a specific form of autocovariance?

Tip: In a WSS process, the second moment of any time instance $t$ is always the same, highlighting the time-invariant nature of WSS processes.