The response of a discrete time system $\mathrm{y}[\mathrm{n}]$ obeys the following relation:

$$ y[n]=\frac{5}{6} y[n-1]-\frac{1}{6} y[n-2]+x[n] . $$

The input to the system is $x[n]=\delta[n]-\frac{1}{3} \delta[n-1]$.

Which of the following options is TRUE for $y[n]$ ?

For a causal discrete-time LTI system with transfer function

$H(z) = \frac{2z^2 + 3}{\left(z + \frac{1}{3}\right)\left(z - \frac{1}{3}\right)}$

which of the following statements is/are true?

Which one of the following pole-zero plots corresponds to the transfer function of an LTI system characterized by the input-output difference equation given below?

$$ y[n]=\sum_{k=0}^3(-1)^k x[n-k] $$