The question is about determining the Region of Convergence (ROC) for a given signal in the Z-transform. To select the correct option, let's first understand some basic principles about the ROC:

1. ROC for a causal signal: If the signal is causal (non-zero for $n \geq 0$), the ROC is outside the outermost pole, i.e., $|z| > r$, where $r$ is the pole's radius.

2. ROC for an anti-causal signal: If the signal is anti-causal (non-zero for $n < 0$), the ROC is inside the innermost pole, i.e., $|z| < r$.

3. ROC for a two-sided signal: For a signal with both causal and anti-causal parts, the ROC will be a ring between two poles, i.e., $r_1 < |z| < r_2$.

4. The ROC cannot include any poles.

The given options are:

• (a) $|z| > 2$
• (b) $|z| < 2$
• (c) $|z| = 1$
• (d) $|z| \neq 0$

Without additional context, the most common ROC scenario is:

• For a causal system, the ROC is typically $|z| > r$.
• For an anti-causal system, it is $|z| < r$.

If $r = 2$, then option (a) $|z| > 2$ would likely be the correct choice for a causal signal.

Would you like more details, or do you have any questions? Here are some related questions for further study:

1. How does the location of poles affect the ROC in the Z-transform?
2. What is the significance of the ROC in determining system stability?
3. How does the Z-transform differ from the Laplace transform in terms of ROC?
4. What happens to the ROC if a signal is neither purely causal nor anti-causal?
5. Can a system have multiple ROCs? If so, what does that imply?

Tip: The ROC for a stable system must include the unit circle ($|z| = 1$).