Consider the compound system shown in the above figure. Its output is equal to the input with a delay of two units. If the transfer function of the first system is given by $$H_1(Z) = \frac{Z - 0.5}{Z - 0.8}$$, then the

A

$$H_2(Z) = \frac{Z^{-2} - 0.2Z^{-3}}{1 - 0.4Z^{-1}}$$

B

$$H_2(Z) = \frac{Z^{-2} - 0.8Z^{-3}}{1 - 0.5Z^{-1}}$$

C

$$H_2(Z) = \frac{Z^{-1} - 0.2Z^{-3}}{1 - 0.4Z^{-1}}$$

D

$$H_2(Z) = \frac{Z^{-1} - 0.8Z^{-3}}{1 - 0.5Z^{-1}}$$