When the input to an LTI system is the corresponding output is (a)...

When the input to an LTI system is

the corresponding output is

(a) Find the system function H(z) of the system. Plot the pole(s) and zero(s) of H(z) and indicate the ROC.

(b) Find the impulse response h[n] of the system.

(c) Write a difference equation that is satisfied by the given input and output.

(d) Is the system stable? Is it causal?