Consider the z-transform X(z) whose pole-zero plot is as shown in figure.

(a) Determine the region of convergence of X(z) if it is known that the Fourier transform exists. For this case, determine whether the corresponding sequence x[n] is right sided, lift sided, or two sided;

(b) How many possible two-sided sequences have the pole-zero plot shown in Figure?

(c) Is it possible for the pole-zero plot in Figure to be associated with a sequence that is both stable and causal? If so, give the appropriate region of convergence.

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Unit circle Re 2.